NBSIR 87-3635

The Characterization of

Microenvironments and the

Degradation of Archival Records:

A Research Program

Elio Passaglia

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Institute for Materials Science and Engineering

Polymers Division

Gaithersburg, MD 20899

October 1987

A Report Prepared for the

National Archives and Records Administration

NBSIR 87-3635

The Characterization of

Microenvironments and the

Degradation of Archivai Records:

A Research Program

Elio Passaglia

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Institute for Materials Science and Engineering

Polymers Division

Gaithersburg, MD 20899

October 1987

A Report Prepared for the

National Archives and Records Administration
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NBSIR 87-3635

THE CHARACTERIZATION OF

MICROENVIRONMENTS AND THE

DEGRADATION OF ARCHIVAL RECORDS:

A RESEARCH PROGRAM

Elio Passaglia

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Institute for Materials Science and Engineering

Polymers Division

Gaithersburg, MD 20899

October 1987

A Report Prepared for the

National Archives and Records Administration

U.S. DEPARTMENT OF COMMERCE, Clarence J. Brown, Acting Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
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EXECUTIVE SUMMARY

El. INTRODUCTION

The National Archives and Records Administration stores an enormous

volume of records, and protecting them from degradation is a matter of great

concern. Because the temperature and the condition of the atmosphere in the

storage areas are important in controlling the rate of degradation of the

stored records, these areas (the "stacks”) have temperature and humidity

control. However, atmospheric pollutants such as particulate matter, NO^^ , SO2 and ozone cause degradation of records, (see, e.g. reference (1)), and while in

some cases the removal of air pollutants from the external air by the NARA air

conditioning system is efficient, in other cases it is not (2), with the result

that the concentrations of S 02 ,and NO^^ in the stack atmosphere are above

recommended levels (3,4).

However, in the stacks, records (with the exception of books) are stored

in containers, and not exposed directly to the ambient environment. The records

experience a "microenvironment" which is possibly less aggressive than the

macroenvirenment of the stacks. Certainly the use of containers protects the

records from particulate matter. If this microenvironment in fact is, or could

be made to be, less aggressive, then expensive changes in the air conditioning

system might be obviated. For this reason, and because of the intrinsic

importance of the topic, a National Academy of Sciences committee convened

specifically to study the problem of the preservation of records, made the

following recommendation(4)

NARA should conduct a study of archival containers and

microenvironments, including boxes, folders, and polyester

encapsulation, with a view to understanding the maximum benefit

that can be obtained from particular materials and designs. The

committee feels that this is an unexplored area that may yield

results highly significant to NARA's preservation efforts.

This report analyzes what is involved in a research program to carry out

that recommendation. The main part of the report is concerned with air

pollutants; temperature and water vapor are discussed in an Addendum. An

analysis the microenvironments experienced by records (principally in

containers) is made then the ability to predict useful lifetimes from data on exposure to air pollution is discussed. Finally, there is laid out a suggested

research program responsive to the recommendations of the NAS Committee, and

which can provide information on the basis of which NARA can make informed

judgments about what actions take to further their protection of historical

records . This program is described in its entirety in the final section of

this summary. It consists of six elements which can be carried out

independently. Depending on resources and priorities, some elements of the

program can be omitted.

E2. Models and Microenvironments

Unless the container that contains documents is impermeable to matter and

heat, the microenvironment experienced by records is not constant, and changes

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as the macroenvironment of the stacks changes. Material can be exchanged

between the microenvironment inside the container and the macroenvironment

outside of it by diffusion through the walls of the container or any gaps or openings in them, or, if there are gaps or openings, by pressure or temperature

changes. However, the container will slow down and dampen those changes and

thus can, at least in principle, provide protection of documents. With complete

sealing, or encapsulation, new and serious effects may arise because of the

possibility of autocatalytic degradation caused by the degradation of the

enclosed documents.

To study these effects, several mathematical models of the actual

situation were analyzed to determine the microenvironments and changes in them

in various situations. These models were

1) An empty container. This is not a situation that arises in practice,

but was analyzed for orientation purposes. As will be seen, the results

are quite instructive.

2) A container holding reactive contents.

3) Containers with reactive walls.

4) Books and folders.

5) Sealed, impermeable containers; encapsulation.

6) Recesses.

/ 7) Temperature and Water Vapor. (Discussed in an Addendum.)

Each of these is discussed in a separate section of the report. The

approximations, both mathematical and physical that had to be made are

discussed in detail there. Because of these approximations, the numerical

results obtained have only qualitative or semi -quantitative significance. It is

felt, however, that the conclusions drawn from the analysis will be valid. The

container used as a prototype in the calculations is shown in Fig. 1. It is

style F in the NARA specifications for archival boxes.

The analysis was done for an isolated container, not one stacked on

shelves with others. This is the most severe condition. The results are easily

translated to stacked containers.

In this summary, only the conclusions of the analysis will be presented,

with only enough discussion to place them in context.

E2.1 The Empty Container

This model is the simplest that can be devised. It is useful for

orientation purposes and to provide the relative importance of the three

mechanisms of transport into and out of the container. As mentioned above,

these are diffusion through the walls; diffusion through gaps; and transport

through gaps by pressure and temperature changes -- called the "breathing"

modes

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If 3L container with an interior atmosphere at a given concentration is

suddenly placed in an external atmosphere that has ten times the concentration

of pollutant, the concentration vs. time curves for the interior concentration

are given in Fig. 3. If the concentration change is different from the factor

of ten used here, the curves are easily scaled. The time scale for the process

remains the same. The right hand curves are for diffusion through the wails for

two values of the diffusion constant, and for the empty container and one

filled with inert documents. The left hand curves are for diffusion through

gaps. The important point is that diffusion through gaps, for this particular

container is about 1000 times as fast as diffusion through the walls, and that

equilibrium with gaps is established in a few hours. Pressure and temperature

cycles of the idealized kind shown in Fig. 5, with the pressure changing from

29 in. Hg to 31 in. Hg with a weekly cycle, and the temperature varying from

19C to 20C with a daily cycle, cause equilibration to occur at approximately

the same time scale as diffusion through the walls. The curves are given in

Fig. 6 . The principal conclusions to be drawn are

1. For gaps or openings of the size in the prototypical container,

diffusion through the gaps is much faster than diffusion through walls.

Indeed, diffusion through the gaps is so fast that for all practical

purposes the container might as well be open. This is a result of the

high diffusion coefficient of gases.

2. Pressure and temperature driven transport, for the temperature and

pressure excursions considered here, are about as effective as diffusion

through the walls as a means of transport.

3. If the exterior concentration cycles (as it does for N0,j in the NARA

stacks) , for a container without gaps the cycling inside the container is

very small. For the container with gaps, the cycling inside the container

is about the same as it is outside.

4. The time scale of the changes is given by Vi/ADS, where V is the

volume of the container; i the thickness of its walls or gaps; A the area

of the walls or gaps; D the diffusion coefficient of the walls or gaps;

and S is the solubility of the pollutant in the wail material. Hence the

time scale is determined by the dimensions of the container through V, 2,

and A, and by the material of construction through D and S. Note that the

quantity A (and i for gaps), and hence the time scale of the changes,

will depend on how the containers are stacked.

E2.2 The Container With Reactive Contents

The model considered here is a container holding contents that can react

with the pollutant. Entrance of the pollutant into the container is by

diffusion, either through the walls or gaps. The example used is SO2 in paper.

As discussed in Sec. 2.9 of the report, SO2 first diffuses into paper, then is

converted by a metal catalyzed reaction into SO3 and thence sulfuric acid,

which then catalyzes the hydrolysis of paper, leading to degradation. Thus,

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when a container holds paper docximents , SO2 that enters the container will

diffuse into the documents and then react to form SO3

. Approximate values of

both the diffusion coefficient and the reaction rate constant are deduced in

Sec. 2.9. The interior concentration of SO2 is thus controlled by both its rate

of entry and its rate of reaction. Moreover, knowing the microenvironment, the

increase of reacted SO2 (i.e.

SO3 ) in the paper can be calculated. This is

done in Sec. 2.6. The important assumption that was made was that the contents

were loosely packed so that diffusion of SO2 into them was not the rate

determining factor.

The results are shown in Figs. 7-10. The situation analyzed is as follows. At a given time, documents which are at equilibrium with their

surroundings are place in a container, which is then closed. Fig. 7, for

diffusion through wails shows what happens to the microenvironment for two

different values of the reaction rate constant. At first the concentration of

SO2 in the box does not change as the SO2 in solution in the contents reacts.

As this is used up, the concentration in the box decreases, eventually reaching

a value determined by a combination of reaction rate and the rate of diffusion

into the container. For the slow reaction rate, diffusion maintains a value of

the concentration of about 0.6 of the original, but for the more rapid

reaction, the concentration drops to the very low value of 0.0044 because

diffusion cannot keep up with the reaction rate at any higher concentration.

Fig. 8 is the same except that diffusion is through gaps. Here, in both

cases, diffusion can just about keep up with the rate of reaction. The contents

might almost as well be in the open.

Figs. 9 and 10 give the concentration of reacted species in the paper as

a function of time. Fig. 9, for diffusion through walls, shows that reaction

proceeds as the original SO2 in solution is used up, then levels off, and then

proceeds at a lower rate. (Note that this is a doubly logarithmic plot.) For

the high reaction rate, considerable protection is provided, but less so for

the slow reaction rate. If the box were impermeable, i.e., the diffusion

coefficient were zero, complete protection would be provided, but then other

problems, discussed under "Impermeable Containers; Encapsulation", would be

encountered.

Fig. 10 is the same as Fig. 9, but for diffusion through gaps. The

reaction rate is just about what it would be in the open. Essentially no

protection is provided.

The significant conclusion drawn from this analysis is that containers

can provided protection from the macroenvironment, but provided they have no gaps in them. As is evident a priori and is shown by the analysis, reaction

cannot proceed more rapidly than material is provided by transport into the

box. It follows that if containers are impermeable, complete protection from

pollutants is provided, but then other and possibly serious problems arise as will be discussed later under "Sealed Impermeable Containers; Encapsulation",

E2.3 The Container With Reactive walls

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Of the various cases investigated, this one appears to hold the most

promise for the protection of documents. The reason for this is easy to see. If

the container reacts with the pollutant as it diffuses through the walls, then

the pollutant may never get into the container. In due course the container may

be destroyed, but the contents would have been protected. The container is

sacrificed to save the contents, much as is a sacrificial anode in corrosion

protection.

This may already be the case with at least some of the NARA containers.

Archival boxes of the type chosen as prototypical containers are already

specified to contain 3% CaC03 . Ail experts consulted on this project have

remarked that SOg an NO2 would react with the CaCOg in their passage through

the wails, and ozone would probably react with the walls even if there were no

CaCOg present. Moreover, if there are any gaps, but if they are long and

narrow, protection could still be provided, for in the passage of a pollutant

through the gap, it could diffuse to the container walls and there react with

them, preventing its entry into the container.

The important model solved in this problem is a container with reactive

walls filled with reactive contents. Unfortunately, mathematical difficulties

preclude the solution to this problem to give concentration- time curves like

those previously described. The best that could be done within the time and

resources available was a solution at steady-state, i.e., after all transients

had died out. The results are given in Table 6. In this table, the reaction

rate constant of the contents is k^ and that of the walls is k^ . Then, various

values of these quantities were investigated. They represent a box made of pure

rag paper holding pure rag contents at the one extreme, and a box made of

newsprint holding newsprint contents at the other. The important result is in

the final coliimn of this table. This coliomn gives the rate of reaction of the

contents compared what it would be in the absence of a container. The results

depend on the diffusion coefficient, but except for the case of a pure rag box

holding pura rag contents (not a very likely situation, and one probably not

requiring much attention in any case)essentially complete protection is

provided. Again, however, the autocatalytic degradation problem needs to be

considered, and will be in the section "Impermeable Containers; Encapsulation".

E2.4 Books and Folders

This analysis was directed at the mechanism by which a pollutant attacks

book pages. Simply stated, the problem is, "Does the pollutant diffuse in

through the edge of the book sheets or does if diffuse in between the sheets

and then spread laterally?" It will be clear that the looser the sheets are packed, whether in a book or in a folder, the more likely is diffusion to occur

between the sheets, because the diffusion constant in gases is much higher than

in solids.

This problem was addressed by applying the concept of grain boundary

diffusion used in metallurgy and is discussed in Se. 2.8. To do this, it is

necessary to know the thickness of the intersheet region and its diffusion

constant. This would also be necessary in any other method of analysis. This

thickness obviously depends on how much pressure is applied to the book or to

how tightly documents are packed in folders. But simply to get some bounds on

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the time scales involved, crude measurements were made on the thickness of

books as compared to the sum of the thickness of the sheets. It was found that

the thickness of the books was roughly 10% greater than the total thickness of

the sheets , so that the intersheet region has a thickness of about 10% of the

sheet thickness. Then as an upper limit for the diffusion constant, a value for

diffusion in the gas phase was chosen

The results are totally contrary to experience. They show that if the

diffusion constant were that in the gas phase, after one day or so the whole

book would be permeated by pollutant. The brown discoloration commonly observed

around the edges of book pages, would instead, to the extent it is associated

with pollutants, be uniform over the sheet. To the extent that these very crude

results have any meaning, they indicate that the diffusion constant between

sheets is more likely to be nearer to that in the solid than in the gas phase.

The whole book acts almost like a solid block of paper. The inter- sheet region

is very likely a quite complicated thing, perhaps corresponding to diffusion

through a percolation maze.

On the other hand, the results do indicate that if sheets are loosely

packed, then the high diffusion constant in the gas phase assures that they

quickly become permeated with pollutant.

E2.5 Sealed, Impermeable Containers; Encapsulation

As has been seen from the analysis of various models, and is obvious a priori . if record documents are placed in sealed containers impervious to

pollutant, then they are protected from the pollutant. The question then

naturally arises, "Why not store records on sealed, impermeable containers?"

Experience has shown that unless the paper stored is of high quality and

resistant to degradation (like the pure alpha- cellulose paper in the

Constitution and Declaration of Independence cases , or photographic print

paper), sealing or encapsulation is harmful. Moreover, sealing good paper with

poor paper may be harmful for the good paper. The reason for this is the

degradation products of the poor paper. These products appear to be acidic and

hence catalyze degradation by hydrolysis, leading to an autocatalytic

situation. The contents of a sealed, impermeable container "stew in their own

juices", so to speak.

While this is the opinion of ail the experts consulted in this project,

laboratory data on this effect are scanty. Only two experiments comparing the

rate of degradation in a sealed capsule with that in the open but otherwise

identical conditions are known to us (27,28). In one of these (27), degradation

was carried out at elevated temperatures in a sealed glass ampoule and compared

to degradation in the open, but otherwise the same conditions. Degradation was

more rapid in the ampoule, but this is not a definitive test because the

pressure (particularly of oxygen) was higher in the ampoule than in the open.

In the other experiment (28), degradation in polyester envelopes was compared

to degradation in the open. It was found that degradation was more rapid in the

envelope. However, it was found that the acceleration of degradation inside the

envelope could be eliminated by including in the envelope paper with an

alkaline reserve. This indicates that whatever the degradation accelerating

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substances are, they are probably acidic, and may be transmitted via the gas

phase

The identification of these substances, and of methods of inhibiting them

are considered to be projects of high priority.

E2.6 Recesses

There are nximerous regions or spaces, e.g., an empty shelf, or the region

over the tops of books packed on shelves, that have limited access to the

ambient stack environment. These spaces, which are referred to as "recesses",

provide for the possibility of a microenvironment, and an analysis was carried

out to see how much this microenvironment differed from the macroenvironment of

the stacks.

In many, and perhaps most, cases, these recesses can be considered to be

a rectangular parallelipiped open on one side to the ambient stack atmosphere,

and with the other five sides consisting of impermeable material. It is clear

that the slowest mode by which this recess can exchange pollutant with the

ambient stack atmosphere is by diffusion; any convection that takes place will

only hasten the exchange. Hence a diffusion investigation was made of this

recess

This is a standard problem in diffusion. It is readily shown that, under

quite unrestritive conditions, the rate at which pollutant spreads into the

recess is independent of the lateral dimensions of the recess. It was then

calculated that for a recess one meter deep, after 12 hours the environment at

the bottom of the recess is essentially the same as the ambient environment.

Any convection that may take place will shorten the time needed to arrive at

equilibrium.

E2.7 Temperature and Water Vapor

These microenvironments are treated in an Addendum. Temperature is

important because it influences the rate of chemical reactions, specifically

degradation reactions in this context. Temperature distributions following a sudden change in temperature were calculated for the case of an isolated book;

a container tightly packed with documents; and a shelf of books. Results for

the temperature distribution as a function of position and time are given in

Figs. A“1 to A- 3. From these, knowing the rate law for a given reaction, the

extent of reaction as a function of position can be calculated. The important

result was derived that in a macroenvironment in which the temperature varies

the extent of reaction at the surface of any one of these items will be greater

than in the interior.

The analysis for water vapor largely follows that for pollutants. The

methods are the same, but the data are even more scanty, and somewhat more

drastic approximations had to be made. The well-known high solubility of water

vapor in cellulose dramatically lowers the rate at which a box filled with

paper documents comes into equilibrium with the external environment as compared to an empty box. In effect, the documents enormously increase the

volume of the box. Also, water participates in hydrolysis, but there is so much

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water in paper that very little is used up during the hydrolysis. For this

reason, and because the initial conditions upon storage are not usually known,

impermeable containers are not practical for controlling moisture content.

E2.8 Conclusions

There are several conclusions that can be drawn from the analysis and

that are very likely independent of the assumptions made in it.

1) The microenvironment inside a container communicates with the

macroenvironment outside it by diffusion through the walls of the

container; by diffusion through any gaps or openings in those walls; or by pressure or temperature changes if there are gaps in the wails.

2) For an empty container with inert walls, the interior microenvironment

eventually becomes the same as the macroenvironment if the latter is

constant, or its average if it is fluctuating. If there are any gaps in

the wails, the interior environment is always very nearly the same as the

exterior environment, and follows any changes in the latter with only a small time delay. The time constant, or "relaxation time", for any

changes in the microenvironment in the absence of gaps in the wails is

given by Vi/ADS, and hence depends on the design of the container through

V,A, and i, and on the materials of construction through D and S. If

there are any gaps, the expression for the relaxation time is the same

but without S, and its value is very small compared to diffusion through

the walls.

3) Pressure and temperature cycles, for the ranges of change and time

scales assumed for those changes, are about as effective as diffusion

through wails in providing communication between the inside and outside

of containers

4) If the container holds reactive contents, i.e., the contents react

with the pollutant(s) in question, then, in the absence of gaps in the

walls, the microenvironment inside the container can be substantially

different and more benign than the macroenvironment outside it. If gaps

are present, then the microenvironment can be essentially the same as the

macroenvironment

5) If the container walls can react with the poilutant(s) in its (their)

passage through them, then essentially complete protection from the

pollutant can be provided. This may even hold if there are gaps in the

walls, provided the gaps are long and narrow.

6) The diffusion constant for the interface between sheets in a book is

probably much lower than for diffusion in a gas, and may approach the

diffusion constant in the solid phase.

7) Sealed, impermeable containers will obviously prevent any

communication between the inside and outside of the container and hence

provide complete protection from the exterior pollutants. However, if the

contents are reactive, they may give off degradation products that

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catalyze further degradation. (The contents "stew in their own juices").

The option of sealed, impermeable containers is limited to such items as very high quality paper, safety film, and perhaps magnetic recording

tapes

8) Unless recesses are very deep, the microenvironment in them is

essentially the same as the macroenvironment.

9) There is a very limited availability of data in the literature with

which to make calculations from the models and to check them.

10) Because of the Arrhenius dependence of rate constants on temperature,

in a fluctuating temperature environment the extent of reaction in the

surface regions of books and document boxes will be greater than in the

central regions of the items

11) The high solubility of water vapor in cellulose dramatically lowers

the rate at which the interior of a box filled with paper documents comes

into equilibrium with the external environment as compared to an empty

box.

E3. Degradation and Its Prediction; Data Availibility

This section is concerned with the prediction of permanence-- the so- called study of accelerated aging. The primary focus is on degradation caused

by air pollutants, and the principal interest is paper. Unlike the previous

section of the report, no analytical work is done; the discussion is primarily

a review of the literature. First there is a general review of paper

degradation; then a review of degradation by air pollutants; then a general

discussion of accelerated aging and a specific one on air pollutants; then

finally a literature survey of transport coefficients and reaction rate

constants- for pollutants in various polymers.

The course of degradation is broken down into three steps. First, and

most basic, there are chemical reactions, e.g., hydrolysis of cellulose. These

lead to what are termed "chemical measures" of degradation, e.g., the decrease

in degree of polymerization. These in turn lead to "physical measures" of

degradation, i.e., those properties of paper that affect its performance in

service, e.g., fold endurance. Now, a pollutant reacts with paper leading to a chemical change (a chemical measure of degradation) which mav lead to a physical change (a "physical measure") that makes the paper no longer useful.

In the ideal world, the relationship between these three: basic reaction,

chemical measure, and physical measure, would be known, and accelerated aging

tests could be devised on a logical, scientific basis. But even in the absence

of this knowledge, this ordering provides a logical skeleton for the analysis,

and is the point of view adopted in the discussion.

The summary of the review is best expressed by the conclusions, which are

as follows

1. Degradation can be characterized by a number of chemical and physical

measurements. The chemical measures are closer to the basic chemical

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reactions that occur on degradation, but the physical measures are more

closely related to the actual utility of record documents.

2. The relationship of the physical measures of degradation to the basic

chemical reactions that occur in degradation are known in only a qualitative way. To put accelerated aging on a firm basis, this

relationship should be determined insofar as possible. This is likely to

be a long and continuing task.

3. The degradation products of paper and other record materials are known

or suspected to increase the rate of degradation, and hence to cause

degradation to be autocatalytic . What these degradation products are is

not known. It is suspected that in the case of paper they are acidic and

promote further degradation by hydrolysis. It is not known if they are gaseous and hence capable of transmission through the gas phase.

4. Sulfur dioxide in paper acts by conversion to SO3 , and thence to

sulfuric acid. The rate of this reaction is increased by heavy metal

ions. This increased acidity causes an increase in the rate of hydrolysis

and hence degradation of the paper. Its action on other record or container wail construction materials is not known. It may be inert in

some of them.

5. The reactions of NOj with cellulose are rather well known, but their

relationship to the physical measures of degradation in paper are not.

Data on transport properties are not known to us.

6 . The action of ozone on records has not been studied. It is known to

degrade cotton fabrics under certain circumstances, and to react with

cellulose, but its effect on the physical measures of degradation is not

well known.

7. The accelerated aging of paper without consideration of the action of

pollutants has been a study of long duration, and has resulted in two

useful standards. Two important questions remain: the effect of humidity,

and the effect of degradation products, which are clearly of central

importance if degradation in sealed containers is to be predicted.

8 . There are only a few experiments directed at the accelerated aging of

paper in the presence of pollutants, and none on other materials of

interest as either record or container wall materials. As a simple

example of the type of experiment that has not been done, consider the

following. The rate of reaction of a pollutant can be increased by

raising the concentration or by raising the temperature. However, raising

the temperature decreases the solubility, which decreases the rate of

reaction. Thus, by simply changing the temperature or concentration

alone, their relative effects will not be sorted out.

9. The availability of data on transport properties and reaction rate

constants is such that these will have to be determined on the actual

materials under investigation when experimental investigations are carried out.

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E4. A RESEARCH PROGRAM

E4 . 1 Introduction

It is clear from the structure of this report, and is evident ^ initio . that the problems of concern in this whole question of microenvironments fail

into two areas:

1. What are the microenvironments experienced by record documents?, and

2. Given an environment, micro or macro, how rapidly do documents

degrade?

The aspects of the environment that are of concern are temperature, relative

humidity, pollutant concentration, and the important question of the presence,

nature, and action of degradation products. The principal emphasis here is on

pollutants and degradation products. Logically, then, the research should

address these two areas. This follows the structure of the report, and since

conclusions were given at the end of the two main sections of the report, it is

necessary to develop a research program that answers the questions posed in

those summaries. Here we describe such a program.

E4.2 Microenvironments

In this section of the report a number on models that relate the

microenvironment inside a container to the macroenvironment (and any changes in

it) outside it were developed. If (a significant "if") these models were known

to be correct, then a knowledge of the container dimensions, and the relevant

parameters D, S, and k for the various pollutant/container wall combinations

would permit the calculation of the microenvironment inside the container. But,

as detailed in Sec. 2, a number of approximations had to be made in the

development of the models, so their validity has to be checked. Hence an

experimental program, supported by theoretical analysis, to check out the

models should be considered. While this program might be called, "validation of

the models", it should be noted that a great deal of important information on

microenvironments will be developed, whatever its intent. Specifically the

following experimental investigations are suggested. This largely follows the

analysis in the previous text.

E4.2.1 The Container with Inert Wails

This is the simplest of the investigations. While it is probably not

applicable to the paperboard container used as a prototype in the report for

illustrative purposes, since its wails are probably reactive, it is likely

applicable in other cases where the wail materials are inert. This, in turn, is

likely to occur only with SO2 , since, as was seen, NO2 and O3 are quite

reactive. The objective of the investigation is to determine, in this simplest

case, how the microenvironment inside the container is affected by changes in

the exterior macroenvironment. As far as is experimentally possible, actual

ES-11
containers should be used. The effect of gaps should be studied, for, as was

seen in the development, they are likely to be very important, and the

"breathing" as well as the diffusion modes should be investigated. Experiments

with the container empty and filled with reactive documents should be carried

out.

As part of this investigation the coefficients D,S and k will have to be

determined for the actual pollutants, wall materials and record materials

involved, for otherwise a purely empirical investigation with hardly any

opportunity for significant analysis will result. The important point to note

is that if the models are verified, or an applicable model is developed, then

it is only necessary to measure these coefficients to predict what would occur

in a new and untested situation.

It is possible to do at least a part of this investigation (e.g., the

empty container) without using a pollutant gas. This is strongly discouraged.

Even though it would then be possible to predict what would happen with a pollutant, assuming an applicable model is developed, it would probably not be

wise to proceed without actual experiments with pollutants. Moreover, it is

unnecessary to use non-pollutant materials. Sulfur dioxide with a convenient

radioactive isotope for analytical purposes would appear to be a natural

candidate as a pollutant gas.

E4.2.2 The Container with Reactive Walls.

This is viewed as perhaps the most important investigation that can be

carried out. As noted in Sec. 2.7, if the pollutant cannot be get through the

container walls, then the contents are obviously protected from them. The only

question that then arises is the effect of degradation, products

An experimental program that investigates this question could go as follows. First, determine the diffusion and solubility coefficients, and the

reaction rate constant for one of the wall material/pollutant combinations. In

this case, paperboard with and without CaCOg , and with and without lignin,

would seem to be very appropriate, as would SOj because of the ease of

measurement and because some measurements already exist in the literature (ISIS). Then experiments with an actual container to determine the interior

microenvironment as a function of the exterior macroenvironment could be

carried out. In this case the prototype container, or a similar one, would

appear to be highly appropriate. Experiments with and without contents should

be carried out. The effect of gaps should be investigated, especially the

effect of their aspect ratio, for as pointed out in the text, long narrow gaps

might prevent the entrance of pollutants if the wall material is sufficiently

reactive

A full analysis of the experimental results derived from these

investigations would very likely require a full solution of the time dependent

diffusion problem. (Recall that only the steady state case was used in this

report.) This solution was sketched out in Appendix A- 9. To apply it would

require more theoretical work. This would be desirable but not completely

essential. A great deal of progress could be made experimentally with good

experimental design and analysis.

ES-12
This is deemed to be possibly one of the most rewarding of the

investigations that could be carried out.

E4.2.3 Degradation Products; Encapsulation

It follows from the discussion in Sec. 2.11 and Sec. 3.4 that if

degradation products are not given off, or they do not catalyze further

degradation, sealing documents in impermeable containers protects them from an

aggressive environment. If degradation products are given off and do promote

further degradation, then sealing documents in an impermeable container will

still protect them from exterior pollutants but might compound the degradation

problem by promoting degradation by the degradation products because these are now prevented from diffusing away from the documents. However, if these

products can be removed from the container by the wall material, either by

reaction with them , or because the products can diffuse through the wails, the

container will at least not worsen the situation. Note that neither of these

two kinds of container can prevent the degradation of inherently degradable

materials; the best they can do is not to aggravate the situation. There is no substitute for high quality record materials. The first case, in which the

products can react with the container walls, might apply to the CaCOg filled

paperboard container, while the second might apply to a polyethylene shrinkwrapped book, although in this case the shrink-wrap might not protect the book

from exterior pollutants. This latter situation is in fact a special case of

the situation in Sec. E4.2.1, except that here we are now concerned with

diffusion out of degradation products, and diffusion in of pollutants.

It is the opinion here that not much can be done on this problem until

the degradation products are identified. Are they organic acids, aldehydes,

ketones, nitrogen oxides, or what? Are they gaseous or not, and even if not, do

they exist in the vapor phase? How are they transferred from one document to

another? By diffusion on contact or by transfer via the gas phase?

It is felt that until these questions are answered, only empirical

progress can be made While this could prove useful (see Ref. 28) , it is felt

that modem analytical techniques like gas chromatography -mass spectrometry

provide an opportunity for the identification of these products . An

experimental progeam on their identification would appear to be very much in

order and would begin to answer the vexing questions about the nature and

likely effect of these products.

When considering an experimental program, it should be remembered that

the primary, and perhaps sole, interest here is on degradation products in the

gas phase, for only then is the microenvironment changed. Then the effect of

containers becomes relevant. It is interesting and important to know, for

example, that the C-6 carbon on cellulose is oxidized to a carboxyl on

degradation, but not relevant to the problem of microenvironments. Only if that

carboxyl is subsequently released as, say, formic acid, does it affect the

microenvironment in the container and hence influence another piece of paper

remote from the one in which it originated. An experimental program of this

type should include paper of various types as well as leather, pyroxylin

containing book bindings, and other materials of interest. An obvious follow-up

ES-13
study is the reaction of these products with wall materials and their diffusion

through them.

E4.2.4 The Book Problem; Folders

The problem of the mechanism of entry of pollutants into book sheets was discussed in Sec. 2.8. There, on the basis of a simple calculation, it was

concluded that the interface between sheets in a book is probably of a complex

nature with a diffusion constant that is probably much lower than for gases,

but whose magnitude is hard to estimate. Aside from a more thorough theoretical

investigation, no particular course of action suggests itself. Moreover, it is

not clear that an investigation of this problem would be very useful. It seems quite clear that the more tightly books and documents in folders are packed,

the more the center portions of the sheets would be protected. Their edges, in

the absence of a container, will always be exposed to the macroenvironment,

however tightly packed, and in a container, the problem becomes one of those

already discussed. As a result, no particular research program is suggested.

E4.3 Degradation; Lifetime Prediction

E4.3.1 Introduction

The studies described in the previous section can be relatively shortterm, since they have the well defined goal of validating and/or developing

microenvironment models, or, as in Sec. 4.2.3, of identifying degradation

products. When it comes to the problems of concern in this section, the

research tends to be longer range, with goals that, while capable of

definition, are not as easily capable of attainment. The problems can be

grouped into three categories: the relation of basic chemical degradation

reactions to physical measures of degradation; the chemical effect of

pollutants on record materials; and accelerated aging by pollutants. We will

take up each of these in turn.

E4.3.2 Relation of Basic Reactions to Physical Measures of Degradation

As discussed in Sec 3.2, this is an important area of research since a knowledge of these relationships is necessary to put accelerated on a sound

fundamental quantitative basis. A research program in this area would include

the identification of the basic reactions involved, and the measurement of

their rates and activation energies. While difficult, this is the easy part.

The difficult part is relating these to the physical measures. While, for

example, a great of work has been done on the relationship between tensile

strength and degree of polymerization in cellulose (73)a chemical measure of

degradation which can be in turn related to hydrolysis, very little has been

done on the relationship for the more commonly used measure of fold endurance.

This whole area merits attention, but it should be considered a long-range

continuing study rather than one with a specific end, except possibly in

specific cases.

It should be pointed out, however, that if research on the identification

of degradation products as in Sec. 4.2.3 is undertaken, it could be considered

part of this study as well, for it would go a long way toward identifying the

ES-14
basic reactions and their mechanism.

E4.3.3 Chemical Effects of Pollutants on Record Materials.

This study involves the reactions that occur between pollutants and

record materials as well as their rates and mechanisms. Again, this is

important for the prediction of lifetime in the presence of pollutants and for

the development of accelerated aging procedures.

It will be noted, however, that a part of this information will have

been developed if the research programs described in Secs. 4.2.1 and 4.2.2 are pursued, for carrying out those programs involves the reaction rate constant of

pollutant with both wall and record materials . The present study could be

considered an extension of that work to more pollutant/material combinations,

and carried out in more depth.

E4.3.4 Accelerated Aging by Pollutants.

As was seen in Sec. E3, very little work has been carried out on

accelerated aging in the presence of pollutants, yet it is an important area if

the effect of pollutants is to be known in a quantitative manner. As in the

development of all accelerated tests, the mechanisms and activation energies of

the various reactions should be determined, as well as, ideally, their

relationship to the physical measures of degradation. Some of this information

would have been developed if the work carried in the previous section and in

Secs. E4. 2.1 and E4.2.2 is carried out. Nevertheless, to carry out such a program properly will be a long effort, albeit a worthwhile one. However, it is

also possible to proceed more empirically. Thus, having chosen a record

material-pollutant combination, the effects of concentration, temperature and

humidity could be investigated. The problem here would be in the relationship

of the results of such an investigation to performance in service. There really

is no way to do this without a comparison of the experimental results to

service results as was done for paper. However, such an empirical study could

permit the relative ranking of pollutant/material combinations. The whole

question of sealed tube aging naturally arises in this study, for moisture will

have a profound effect, and such aging again brings up the question of

degradation products

E4.4 Summary and Conclusions.

The research program laid can be grouped into seven elements , which may be

listed as follows.

1. Microenvironment and reaction in a container with inert walls.

2. Microenvironment and reaction in a container with reactive walls.

3. Identification of degradation products.

4. The "Book Problem" and folders.

ES-15
5. Relation of basic degradation reactions to physical measures of

degradation.

6. Chemical effects of pollutants on record materials.

7. Accelerated aging with pollutants.

This program would, in our view, go a long way toward carrying out the

recommendations of the NAS Committee, and go beyond them them in developing the

effect of pollutants on lifetime in service. Setting priorities among the

elements of such a program requires a set of criteria, and many different

orderings can be achieved depending on those criteria. Using the criteria of

relevance to the problem of microenvironments in containers and the probability

of achieving significant results we would place the elements of the program in

the following order : 2, 3, 1,7, 6, 5.

Element 4 is omitted for the reasons given in the previous section. Element 6

is low on the list because a lot of the information that would be developed in

this element would be developed in carrying out elements 1 and 2. Element 5 is

low on the list despite its importance because it should really be considered

to be a continuing background research effort and probably would have only

long-term impact. Elements 1 and 2 are obviously central to the problem of

containers and their utility, and element 3 is central to the problem of

sealed, impermeable containers. Element 7 is placed where it is because of the

importance of predicting performance in service in the presence of pollutants.

Finally, it should be realized that this is a subjective listing based upon one set of criteria. Other criteria would very likely lead to another ordering.

Acknowledgements

The" author is pleased to acknowledge gracious, courteous and uniformly

helpful discussions with Professor Norbert Baer, Professor Glen Cass, Mr. Peter

Waters, Dr. Charleton Bard, Dr. Chandru Shahani, Mr. W.K. Wilson, Dr. Leslie

Smith, and Dr. Alan Calmes and the rest of the NARA staff.

ES-16
TABLE OF CONTENTS

1. INTRODUCTION 3

2. MODELS AND MICROENVIRONMENTS 4

2 . 1 Introduction 4

2.2 Data and the Validity of the Calculations 4

2.3 The Prototype Container 5

2.4 Approximations in the Treatment 6

2.5 Flows Into an Empty Container 7

2.5.1 Diffusion Modes 7

2. 5. 1.1 Constant Exterior Concentration. ..

2 . 5 . 1 .

Exterior Conditions Vary

With Time 10

2.5.2 Breathing Modes.. 11

2.5.3 Discussion and Conclusions 13

2.6 The Container With Reactive Contents 13

2.6.1 Discussion and Conclusions 17

2.7 The Container With Reactive Walls 17

2.7.1 Introduction 17

2.7.2 The Empty Container 18

2.7.3 The Container With Reactive Contents 19

2.7.4 Discussion and Conclusions 20

2.8 The Book and Folder Problem 20

2.9 An Analysis of the Data of Hudson, et.al 22

2.10 Models Not Solved 24

2.11 Sealed Impermeable Containers;

Encapsulation 25

2.12 Recesses 26

2.13 Conclusions 28

3. DEGRADATION AND ITS PREDICTION; DATA AVAILABILITY 29

3.1 Introduction 29

3.2 Paper Degradation 29

3.2.1 General Review 29

3.2.2 Sulfur Dioxide 30

3.2.3 Oxides of Nitrogen ...32

3.2.4 Ozone and Other Pollutants 32

3.3 Leather 33

3.4 Lifetime Prediction; Accelerated Aging 33

3.4.1 General 33

3.4.2 Accelerated Aging With Pollutants 36

3.5 Data Availability 37

3 . 6 Cone lus ions 37

4. A RESEARCH PROGRAM 39

4.1 Introduction 39

4 . 2 Microenvironments 39

4.2.1 The Container With Inert Walls 39

4.2.2 The Container With Reactive Walls 40

4.2.3 Degradation Products; Encapsulation 41

4.2.4 The Book Problem; Folders 42

4.3 Degradation; Lifetime Prediction 42

4.3.1

Introduction 42
42

4.3.2 Relationship of Basic Reactions

to Physical Measures of Degradation

4.3.3 Chemical Effects of Pollutant

on Record Materials 42

4.3.4 Accelerated Aging With Pollutants 43

4.4

Summary and Conclusions. 44

5 . ACKNOWLEDGEMENTS 44

REFERENCES . . 45

TABLES 50

FIGURE CAPTIONS 59

FIGURES

APPENDICES

ADDENDUM
1. INTRODUCTION

The National Archives and Records Administration stores an enormous

volume of records, and protecting them from degradation is a matter of great

concern. Because the temperature and the condition of the atmosphere in the

storage areas are important in controlling the rate of degradation of the

stored records, these areas (the "stacks") have temperature and humidity

control. However, atmospheric pollutants such as particulate matter, NO^^ , SO2 and ozone cause degradation of records, (see, e.g. reference (1)), and while in

some cases the removal of air pollutants from the external air by the NARA air

conditioning system is efficient, in other cases it is not (2)

with the result

that the concentrations of S02 ,and NO^^ in the stack atmosphere are above

recommended levels (3,4).

However, in the stacks, records (with the exception of books) are stored

in containers, and not exposed directly to the ambient environment. The records

experience a "microenvironment" which is possibly less aggressive than the

macroenvirenment of the stacks. Certainly the use of containers protects the

records from particulate matter. If this microenvironment in fact is, or could

be made to be, less aggressive, then expensive changes in the air conditioning

system might be obviated. For this reason, and because of the intrinsic

importance of the topic, a National Academy of Sciences committee convened

specifically to study the problem of the preservation of records, made the

following recommendation(4)

NARA should conduct a study of archival containers and

microenvironments, including boxes, folders, and polyester

encapsulation, with a view to understanding the maximum benefit

that can be obtained from particular materials and designs. The

committee feels that this is an unexplored area that may yield

results highly significant to NARA's preservation efforts.

This report will analyze what is involved in a research program to carry

out that recommendation. Following an analysis of the microenvironments

experienced by stored records (principally in containers) , which is the body of

the report, a discussion of the ability to predict useful lifetimes from data

on air pollution will be given. Finally, there will be laid out a suggested

research program responsive to the recommendations of the NAS committee, and

which can provide information on the basis of which NARA can make informed

judgments about what actions to take to further their protection of historical

records. The main body of the report is concerned with air pollutants.

Temperature and water vapor microenvironments are treated in a separate

Addendum

The plan adopted to arrive at a research program was to model the

I environment inside a container, and to predict what changes occur in that

I environment when changes occur in the exterior environment, always remembering

that the function of a container is protection from harmful substances in the

ambient atmosphere. An analysis carried out by such models can outline the

important features of materials of construction and of container design in a

3
qualitative or semi -quantitative manner, and hence lead to two important

conclusions: The important elements that should be included in a research

program, and the type of protection that containers can provide.

2. MODELS AND MICROENVIRONMENTS

2 . 1 Introduction

Unless containers are hermetically sealed and constructed of impermeable

materials (the document cases for the Constitution and the Declaration of

Independence are outstanding examples of such cases) they will continue to

exchange material between their interiors and the exterior environment via the

gas phase. This may be thought of as a "flow" into and out of the container. If

these flows were known, then the sophisticated modelling methods used by Cass

and others (5,6,7) could be used to predict the rate of reaction of the

contents of the container (i.e.

the stored documents) with components ' in the

environment. This presumes, of course, that the reaction rate constants are known, and as will be seen later, they generally are not. Moreover, even if

these were known, it would still be necessary to relate this reaction to some

measure of degradation. This subject will be discussed more fully in a later

section of the report.

In the present case, the flows into and out of the containers are not

known. Moreover, the flows are influenced by reactions with the contents, and,

very importantly, the wall materials and construction of the containers. Hence,

an integral part of the characterization of microenvironments and the reaction

rate with pollutants of documents inside containers is the determination of

flows into and out of containers. Note that "flow" need not be a gross

macroscopic flow of material, but can be permeation, or diffusion.

A container can exchange material with the ambient environment by three

distinct mechanisms:

1) Diffusion through the wails of the container.

2) Diffusion through any openings or gaps in the container wails.

3) Pressure and temperature driven flow through openings or gaps in the

container walls, this mode can be thought of as "breathing".

Each of these mechanisms will treated, although not in every model presented.

2.2 Data and the Validity of the Calculations

In what follows, a niimber of rather complex calculations, with numerical

results will be presented. These numerical results require such input data as diffusion coefficients, solubilities, and reaction rate constants. Data for

these quantities are largely unavailable, and have had to be calculated or deduced from published material. (In fact, if they were known, the task of

NARA would be largely finished.) As a result, while detailed calculations will

be presented, it must not be assumed that these represent quantitatively what

actually occurs, even allowing for the imperfect relation between a mathematical model and reality. But, while the results may not be

quantitatively correct, it is believed that the principles illustrated will be

correct. Moreover, it must be remembered that there is no substitute for

experimental data. A model should not be believed without experimental

4
verification. On the other hand, an experiment without analysis (often on the

basis of a model) has little utility outside the specific experimental

situation employed.

2.3 The Prototype Container

The NARA has a very large number of containers of various sizes and

shapes used to store records- -documents , films, tapes, etc. Each of these has a specific geometry and is made of a specific material. As will be seen, both of

these factors influence the exchange of material between the interior and

exterior of the container. To model individually each of these containers would

be beyond the scope of this study, and is, moreover, not necessary to obtain

the general principles that are of concern in this study. The general results

obtained with one container can be translated fairly directly to another,

provided the materials property data and dimensions are known. As a result, a prototypical container was chosen. It is style F in the NARA specifications for

archival boxes (8)

This container (or "box" in the NARA specifications) will be used as a basis for calculations. It is generally filled with paper documents of legal

size (8h"xl4"). Hence, the system used for illustrative calculations will be

paper - SO2

. If the data are available for other systems, the results should be

easily translatable.

There are several important dimensions of the container. These are the

total volume, the volxome occupied by the contents, the unoccupied volume, the

area of the surface through which atmospheric components may diffuse into and

out of the container, and the thickness of the wall. Of crucial importance are any gaps or openings in the container walls, for the rate of diffusion in the

gas phase is enormously greater than in the solid phase of the walls. Diffusion

constants in the gas phase are of the order of 0.2 (9), while in the solid

phase they are of the order of

10“^. Hence, while gaps may be small in area, they can be crucially important

as a pathway for communication between interior and exterior. Moreover, gaps

are the means by which material is exchanged by the "breathing" modes discussed

above

An inspection of two boxes provided by NARA showed a number of gaps

These were on the bottom of the sides; between the hinged cover and the side

walls; behind the hinged cover on the front; and at the edges behind the edge

stay. Some of the gaps may be covered up when the boxes are on shelves in the

stack, so it is difficult to estimate precisely the area through which

diffusion can take place, and the length of the diffusion path.

For the purpose of illustrating the importance of gaps , the gap behind the

hinged cover in the front of the box was considered to be the only gap.

The important dimensions of this prototypical box are given in Table 1.

These dimension are for an isolated box, not one crowded on a shelf. For the

calculation of the area, the bottom was omitted. If the box were crowded on a shelf, the area of the front and back would have to be omitted, since these

would not be accessible to the exterior atmosphere. What effect this has will

be discussed at the appropriate points when the results of the calculations are

5
presented. The thickness was taken as constant over the whole surface of the

box, despite the fact that there are two thicknesses on the upper portion of

the box on the sides. The reason for this is that the space between the cover

and the sides is easily accessible to the exterior atmosphere.

2.4 Approximations in the Treatment

As will be seen in the next sub -section, the solution of diffusion

problems forms a large part of this study. Diffusion, and its twin, heat

conduction, are old and well established branches of physical science

(10,11,12). The mathematical basis of the theory is well founded and, for our purposes, there are no outstanding basic questions. However, the application to

specific situations can be mathematically very difficult, so two basic

approximations have had to be made. First is the question of geometry. In its

pure form, the problem of flow into a box is a three dimensional problem. To

solve such a three dimensional problem for all the cases that will be

considered would be extremely time consuming, if possible at all analytically.

As a result, all the diffusion problems have been converted into one

dimensional problems, as will be discussed when the specific models are

analyzed. It is felt that this is not a serious approximation.

The second approximation is the assumption that diffusion constants are independent of concentration. The basic differential equations for diffusion

with concentration dependent diffusion constants are, of course, well known,

but their solution generally requires numerical computation. This might be

appropriate for the solution of a well defined and important specific

situation, but is not appropriate for the broader based treatment required for

the present study. Moreover, in the specific cases when the diffusion of an air

pollutant in polymers has been studied (13), the diffusion constant differs by

about a factor of two with concentration. Considering that we have essentially

no data on the diffusion of pollutants through paper, taking the diffusion

constant to be independent of concentration is not unwarranted.

Another topic is not exactly an approximation, but nevertheless merits

discussion. This is the treatment of the walls of the container as diffusing

membranes. If the wails are polyethylene or polyethylene terephthaiate , this

would hardly be questioned. Such homogeneous plastic films are customarily

treated in this way. The same is done in this report for the paperboard walls

of the prototype container and paper in other forms as well. Paper is, of

course, not a physically homogeneous material, so this may seem inappropriate.

However, a permeability coefficient may be defined and measured for paper, as well as a solubility for various gases and vapors. That is ail that is

necessary to define a diffusion constant, so in this report paper and

paperboard will be treated as a diffusing membrane.

Finally, there is the question of the solubility of pollutants,

specifically SO2 and , in the material of construction of the containers,

and in the contents. The relation between solubility in the substrate and in

the gas phase is assumed to be proportional. As above, the state of knowledge

in the field and the mathematical complexity that would otherwise result make

this a warranted assumption.

6
Definitions of the various symbols used, along with their dimensions and

units, which can often be a vexing problem since various conventions are found

in the literature, are given in Appendix A-1. This appendix also contains a discussion of a materials balance problem that is important in some of the

models that are considered.

Even with these simplifying assumptions, exact solutions to specific

diffusion problems are often quite complex and require computer methods for

numerical calculation. Where possible, these exact solutions are given for the

sake of completeness and because they might be used in subsequent work. In all

cases, when the exact solutions are too complex, simplified solutions are

obtained and used for numerical calculations. The simplifications are described

at the appropriate places in the text.

With this introduction, we are now ready to analyze specific models

which, it is felt, are important to understand if a rational subsequent program

of study is to be developed. In each case mathematical details are relegated to

and Appendix. The body of the text will describe the models, their importance,

and discuss the results

2.5 Flows Into an Empty Container or a Container Holding Inert Materials.

This is the simplest model that can be devised. It is useful for

orientation purposes, and to provide the relative importance of the three

mechanisms of flow into and out of the container already described. To

recapitulate, these mechanisms are:

1) Diffusion through the walls of the container.

2) Diffusion through gaps or openings in the walls of the container.

3) Flow through gaps or openings in the wails driven by temperature or pressure changes --the "breathing" modes.

The first two are both diffusion modes, and will be described first.

2.5.1 Diffusion Modes

2. 5. 1.1 Constant Exterior Concentration

For this purpose, consider a container which is empty, or contains inert,

unreactive material. Then consider a certain pollutant, e.g. SO2

. If the

concentration of this pollutant inside the container is different from the

outside, the pollutant will diffuse through the container walls or through gaps

in them until the concentrations on the inside and outside are equal. The

pollutant will always flow from the region of high concentration to that of

low. The problem addressed is the following: "If the concentration inside the

container is a given value different from the outside, and the latter is

constant, how does the interior concentration change with time?"

First, this problem is changed into a one dimensional problem, i.e.,

diffusion is in only one direction ("inward" if the outside concentration is

higher, "outward" if the outside concentration is lower.) How this is done is

shown in Fig. 2. The container is replaced with a chamber with all its walls but

one impermeable. That wall consists of a permeable membrane representing the

walls of the container, or gaps in those walls, as the case may be. The area,

7
A, of this membrane is equal to the appropriate area in Table 1, and its

thickness, i, is the same as the thickness of the walls, or the diffusion

length in the case of a gap in the wails. The membrane has a diffusion

constant D. The container has an occupied volume and an open volume V. The

concentration of pollutant inside the container is Cj^ , which is a function of

time, while the outside concentration is C2 and, for this model, is assumed

constant. Inside the container, as an approximation, is assumed to uniform

with respect to position (i.e., it is "stirred"), which is a reasonable

assumption considering the rapid diffusion in the gas phase. In the membrane,

the concentration is C and is a function of position and time.

The exact solution of this problem is given in Appendix A- 2 and will not

be repeated here. As shown there, the solution involves the roots of a transcendental equation followed by the solution of an infinite set of

algebraic equations, which, however, can probably reduce to a set of three or four. It was felt that the time it would take to work with this exact solution

(which would be significant since it involves computer programming) would not

be wisely spent, so a simplifying assumption was made.

That assumption was simply that the concentration gradient of pollutant

in the membrane is linear, i.e, changes linearly from its value on the inside

to its value on the outside. This assumption is expected to very good for thin

membranes and less good for thick ones, but in any case to give a reasonable

semi -quantitative solution. With this assumption the equation for the rate of

change of is easily solved. This is done in Appendix A-3. Because the

derivation and solution are very simple, and illustrate the principles

involved, they will be repeated here. The uninterested reader can jump

immediately to the discussion following Eq. 7.

The flux of pollutant through the membrane and into the container, in

amount/unit area/unit time, is given by Pick's first law of diffusion:

where D is the diffusion constant, C is the concentration in the membrane, and

the derivative is taken at x=0 (see Fig. 2). For a linear concentration

gradient, Eq.l becomes

F = ^ C(i) - C(o)

2

where C(i) and C(0) are the concentrations of pollutants in the membrane at x=i

and x=0 respectively, and i is the thickness of the membrane. Now, this flux of

material into the box will increase the concentration there, and this will be

greater the greater the area of the membrane, and lower the greater the volume

of the box. Hence we can write

AD = ^ (C(i)-C(O)) 3

for the rate of change of concentration of pollutant inside the box. Now, for

8
diffusion through a gap, C(0)=Cj^ and C(i)=C2 , hence we get

Cl) 4

For diffusion through the walls, more care is needed because represents the

concentration in the gas phase, while C represents the concentration in the

walls of the box. These must be related in order to proceed. For that purpose,

we define the dimensionless distribution coefficient S (see Appendix 1) as

S=C./C, 5

where and Cg are the concentrations in the solid and gas phases

respectively, and we assume that S is independent of concentration. With these

changes the equation for diffusion through the walls becomes

dCj_

at _“ ^

Vi Cl)

which is the same as Eq.4 except for the factor S.

6

As shown in Appendix A- 3, the solution to Eqs. 4 and 6 is

C1 /C2 = 1 - (1 - C1 VC2 ) exp (-t/r) 7

where r is Vi/AD for diffusion through gaps and Vi/SAD for diffusion through

walls, and is the concentration inside the container at time t=0, i.e.,

when the container is closed.

Equation 7 gives the ratio of the concentration inside the container to

that outside as a function of time. This is plotted in Fig. 3 for a value of

C( 0 )=0 . 1 C2 , i.e, at t=0, the concentration inside the container is just 0.1

that on the outside. The effect of choosing other values for this quantity will

be discussed shortly. The values of i,A, and V are from Table 1, so that this

represents diffusion into that specific NARA box. Curves are given for values

of diffusion constants of 10”® and 10”® and for full and empty boxes. The

values of D come from an analysis of the data of Hudson and co-workers (14,

15,16), and will be discussed in a later section of the report.

In each case the curves start from the value of 0.1 (note that the very

early times for the curves for diffusion through gaps are not shown) chosen for

the initial conditions, and rise smoothly to the value 1, at which point the

concentration in the box is the same as the concentration on the outside. As

expected, it takes a shorter time for the full than for the empty box to reach

this value. If a different initial concentration had been chosen, the curves

would have risen smoothly from that value to the value 1 , but the time over

which the change takes would be the same. This is totally controlled by the

parameter r

Most striking is the substantial difference between diffusion through

gaps and diffusion through the walls of the box. Depending on the diffusion

constant in the box wails, diffusion through gaps is 100 to 1000 times faster

9
than diffusion through walls. Thus, for gaps, equilibration is essentially

complete in one day or less, while for walls, for these diffusion constants,

several months to more than one year are required. This striking effect of gaps

will become even more apparent later.

The time dependence of this process is contained in the parameter r of

Eq.7. This serves the function of a "relaxation time" for the process, and

values for the six curves are given in Table 2. It can be seen that the value

of these relaxation times, which roughly represent the time scale over which

changes take place, reflect the statements just made. The value of the

relaxation time is determined by the geometry of box through V,A, and i,and by

the material of construction through D and S.

2.5. 1.2 Exterior Conditions Vary with Time

The calculations presented in the preceding section were interesting and

led to an important conclusion about the effect of openings in the box wails,

but they were rather artificial in that they assumed the concentration of

pollutant in the air outside the box was constant in time. This is, of course,

not the case. The concentration of pollutants in the stack atmosphere is known

to fluctuate (2)

and, in the case of , to follow the diurnal variations in

the ambient District of Columbia environment (2). Hence, in this section we

answer the question, "What happens when the exterior concentration is not

constant?" Recall that we are still dealing with an empty container or one

filled with inert documents.

Again the process has to be modelled. For that purpose we consider that

the concentration of pollutant in the stacks varies in the manner of NO^ as determined by Hughes and Myers (2)

We further simplify this by assuming a sinusoidal variation with a period of twelve hours. A sketch of the assumed

variation is shown in Fig. 4. It will be noticed that Cg is the average

concentration and Cj is the time varying component. While this is a simplification, it should be mentioned that the methods of analysis to be

described could easily be used for an accurate Fourier series representation of

the actual time variation of the concentration. This was not done because the

added mathematical complexity would not have added sufficiently to the insight

gained from the simpler model adopted.

This model is solved in Appendix A-4. An exact solution could be obtained

by the methods given in Appendix A- 2, but this was not pursued because the

mathematical complexity would have precluded its use in this study. Again the

approximation of a linear concentration gradient in the walls or in any gaps

was made, and the resulting expression for the time rate of concentration

inside the container is

This is the analogue of Eq. 7, and all other terms are the same as there and in

Fig. 4, except for w and 6 . The former is 27r/period of the variation, and S is

given by

Sin(ci;t-t-5)

8

10
tan5 = -wr 9

Its meaning will be discussed in the next paragraph.

It will be seen by comparing Eqs. 7 and 8 that the latter is exactly the same as the former, except that it contains an added term which is sinusoidal.

What this means is that the time variation of concentration is exactly as given

in Fig. 3, except that there is added to the curves a ripple caused by the

sinusoidal variation of the exterior concentration. The period of this ripple

is the same as that of the exterior (i.e.

twelve hours), and its magnitude is

Cf/Cc(l+ci)^r^ ) . It is out of phase with the exterior fluctuation, the phase

difference being given by the quantity S , which essentially gives the time

difference between peaks in concentration in exterior and interior.

The quantity that governs the magnitude of the interior ripples is

(l+«^r^). The r are the relaxation times given in Table 2, and in Table 3 we give the values of (l+w^r^). First we describe the situation with diffusion

through wails. Here the values range from 48.7 to 20,000. Hence, in the worst

case (a full box with diffusion constant of 10’®), the amplitude of the ripple

is about 1/50 of the exterior amplitude. This would hardly be visible on the

graphs of Fig. 3. In the best case the amplitude is a totally negligible

1/20,000 of the exterior amplitude. Thus, for diffusion through walls, at least

for the values of the constants chosen, the interior concentration rises

smoothly from its initial value to the average concentration in the exterior

with hardly a discemable ripple, as do the curves in Fig. 3.

The situation when a gap is present is far different. Then the value of

1-Kt)2r^ is essentially unity for both full and empty boxes. This means that the

concentration inside the box is essentially the same as in the exterior. The

ripple to be added to the appropriate curves in Fig. 3 has the same magnitude

as the variation in the exterior. After the transient has died out (about one

day, see Fig. 3), the interior environment is exactly the same as the exterior,

and the box provides no shielding from the macroenvironment. Considering that

the two relaxation times are approximately 25,000 sec. (7 hours) and 5600 sec. (1.5 hours) while the period of the oscillations is an assumed 12 hours, this

is just what would be expected.

2.5.2 Breathing Modes

It will be recalled that breathing modes were the mechanisms by which the

interior of a container could exchange material with the exterior by pressure

and temperature changes. This, of course, requires gaps or openings in the

walls of the container. To make clear the mechanism of these modes, consider

pressure first. Let the atmoshperic pressure change. It is assumed that the

container has rigid walls and that the pressure in it is always the same as the

atmospheric pressure, air being drawn into or exhausted from the container to

maintain this condition. For the purpose of visualization assume that the

atmosphere has a concentration of pollutant higher than that in the container.

When the atmospheric pressure increases, and assuming the temperature remains

constant, air flows into the container. This air carries pollutant with it, and

this will increase the concentration of pollutant in the container. Now let

the atmospheric pressure decrease, again assiaming constant temperature. Air

will be exhausted from the container, but this will not change the

11
concentration

Repeat the cycle many times. Eventually the concentration in the

container will the same as the exterior concentration, and any further cycling

will not change it.

Temperature changes work the same way. Assume the atmospheric pressure

remains constant. Now decrease the temperature. The only way a constant

pressure can be maintained in the container with constant volume is for the

amount of air in the container to increase. Hence air will be drawn into the

container, changing the concentration. Conversely, as the temperature

increases, air will be exhausted from the container, but again the

concentration will not change. Eventually, the concentrations inside and

outside the container will be equalized.

The problem we ask, with either of these mechanisms, is , "How does the

concentration vary with time?" For this it is necessary to model the

temperature and atmospheric pressure changes. The model that was chosen is

shown in Fig. 5. Either of these two variables cycles, its value rising

linearly from an initial value or T^ to a final value Pj and T^ , and then

drops linearly to the same initial value. Actually, it is not necessary that

the rise and decrease portions of the cycle be linear, nor that they have the

same length in time. Ail that is necessary is that they be monotonic.

The breathing model is solved in Appendix A- 5. There it is shown that the

ratio of the interior to the exterior concentration for pressure cycles is

Cj_

C2 = 1 10

where N is the number of cycles, and for temperature changes the completely

analogous expression

11

is obtained. Note that i and f are interchanged in these equations. The reason

is that air enters the container when the pressure increases . but enters when

the temperature decreases

Note also that when N=0 (at the start of the

process when the records are boxed), Ci=C^g . Now, P^/Pf and Tj/T^ are both less

than unity. Hence for very large N, Cj^=C2

. Finally, it should be noted that the

size of the box, its dimensions, and the materials of construction do not enter

into these expressions.

To illustrate this behavior we assume that the atmospheric pressure

varies with a weekly cycle, and that P^ and Pf are 29" H^ and 31" H^

respectively. Similarly, for the temperature, a one day cycle with T^=293K and

Tj=292K, representing a temperature fluctuation of approximately two degrees

Fahrenheit between night and day. A more accurate estimate obviously could be

made using the stack temperature records.

The results are plotted in Fig. 6 on the same scale as Fig. 3 so as to

12
make comparison easy. It is seen by comparing these two figures that the

breathing modes are quite slow (at least for the conditions assumed here) and

amounts approximately to the flow caused by diffusion through walls with a diffusion constant of 10“

2.5.3 Discussion and Conclusions

The change of concentration with time inside a box has been calculated

for diffusion through the walls and through gaps in them for constant and

fluctuating exterior conditions. The breathing modes of the box have also been

calculated. It has been found that for reasonable values of the diffusion

constant and solubility in the walls, diffusion through gaps in the walls is by

far the most efficient process for exchanging material between inside and

outside of a container. This is the expected result given the values of

diffusion constants in gases as compared to solids. Indeed, the calculations

show that if there are significant gaps or openings in the walls, containers

provide little, if any, protection from the outside environment, except

possibly for protection from particulates

Even for diffusion through walls, the concentration of pollutant inside

the box eventually reaches the level in the exterior, and hence it might be

thought that containers provide no protection, at least for very long times.

The next section will show that this is not the case. The reason is that the

present calculations were for an empty case or one filled with inert materials

If the contents of the container are not inert but instead react with the

pollutant, then their presence will affect the diffusional flow into the

container. Moreover, they obviously cannot react more rapidly than material

flows into the container, and thus the container can at least in principle

provide protection. If, for example, the container were hermetically sealed and

made of a material through which the pollutant cannot diffuse (e.g. glass or

steel)

then obviously complete protection would be provided. But then, as will

be seen in a later section of the report, new and serious problems arise.

2.6 The Container With Reactive Contents

The problem that will be addressed in this section is that of a container

that holds documents that react with the pollutant in question. This is clearly

a more realistic representation of reality than the models of the previous

section, for there would be no problem if the contents of the container were

inert

Again, however, assumptions about the situation have to be made if the

model is to be solved with the resources available in the present study. Hence

the following assumptions are made:

1. The contents react with the pollutants in a first order reaction.

2. The reaction is not diffusion limited; i.e., the rate of reaction is

not limited by the rate of diffusion of pollutant into the records. This

seems to be the case in the experiments of Lyth-Hudson and co-workers

(14-16) on paper and SO2 , which is one of the principal systems of

concern. These experiments will be discussed and analyzed in a later

section of the report.

3. Because of the previous assumption, the contents are taken as loosely

13
packed, for if they were not, diffusion might be the rate limiting

process

An exact solution for this model is given in Appendix A-6. Again, this

is given for reference only, and will not be considered further. An approximate

solution, using the same approximation of a linear concentration gradient in

the container as used in the previous section is given in Appendix A- 7 for a constant exterior concentration of pollutant, and in Appendix A- 8 for a fluctuating exterior concentration.

In this case there are two quantities that can be calculated: the

concentration in the gas phase inside the container as a function of time, and

the concentration of reacted materials in the container contents , again as a function of time. As shown in Appendix A-7 for constant exterior concentration

the equation for the concentration is

and for the concentration of reacted material in the container contents is

All the quantities in these equations have the same meaning as in Eq. 7 of the

last section, and V^. is the volume of records. However, care must be taken

with the total volume, V. This represents the total volume available to the

unreacted pollutant in the box. Now, as discussed in Appendix A-1, the

unreacted pollutant can be in the gas phase, which is the unoccupied volume, or in solution in the contents, in equilibrium with the gas phase. The former is

simply the volume of the empty space in the box. The latter is, however, SV^

which can be quite large for large values of S. The sum of these is the volume

V. In effect, this substantially increases the value of the relaxation times as compared to the treatment in the preceding section. There are now, moreover,

two relaxation times. The first, r^, pertains to diffusion through the walls

or gaps in them, and, as before is given by Vi/ADS. The second, T 2 , pertains

to the rate of reaction of the contents with the pollutant, and is given by

V/VgkS, where is the volume of contents, and k is the first order reaction

rate constant. The behavior of the concentration in the gas phase will be

discussed first.

As compared to the situation with inert contents, there is an important

and significant difference in this case. In the previous case, for very long

times, the concentration in the gas phase was just equal to the exterior

concentration, and diffusion of pollutant into the container stopped. In the

present case, for very long times the concentration in the gas phase approaches

12

X

13

14
the value

_22

1+^1 A2 14

Thus, since both relaxation times are positive quantities, the interior

concentration is lower than the exterior. Hence diffusion into the container

cannot stop. The rate of diffusion of pollutant into the container is just

balanced by the rate of reaction with its contents, thereby keeping the

concentration constant at the value given above.

To demonstrate the behavior of the concentration in the gas phase as a function of time, a graph was made from Eq. 12, and is shown in Figs. 7 and 8

for diffusion through walls and diffusion through gaps, respectively. The

parameters for the calculations are given in Table 4. For this case, the

container was assumed to be half full so that the document sheets are

relatively loosely packed and the assumption that the rate of reaction is not

diffusion limited could be justified. Otherwise, the container is the

prototypical box. The most important parameter, however, is the reaction rate

constant. These are values that were calculated (or deduced) from the

previously mentioned work of Hudson and his collaborators (13 -16) as will be

discussed later in a separate section of the report. In this work, the

"uptake", or sorption, of SOj by paper was studied. The conclusion was reached

that sorption of SO2 , which remained mobile, was followed by conversion of the

SO2 to SO3 , which was then fixed, and presumably catalyzes the degradation of

the paper. The reaction rate constant refers to this conversion, not

necessarily the degradation, as will be discussed later when the degradation of

paper is addressed. Two values are chosen from the values deduced, a low one calculated for pure rag paper, and a high one calculated for newsprint

containing a high percentage of ground wood. Whether the numbers are correct or

not, they at least ought to have comparative meaning and to illustrate the

principles involved. The value of k for the pure rag paper was calculated to be

2.9x10"® and for the groundwood paper the substantially higher value of

830x10"® was calculated.

For all the various curves to be presented, the initial concentration of

pollutant in the gas phase was assumed to be the same as the exterior

concentration, and the paper was assumed to be in equilibrium with this. This

seems a reasonable assumption- -indeed, more reasonable than others which could

be made. The diffusion constant was taken to be 10"® for ail the curves, to

keep the number of results manageable.

Figure 7 gives results for diffusion through walls, and Fig .

for

diffusion through gaps, and in each case the ratio of the interior to the

exterior concentration is plotted as a function of time, with time on a logarithmic scale. Referring first to Fig. 7, the curve for the pure rag paper

drops smoothly from a value of unity to a value of 0.56, but requires more than

a year to do so, while that for the groundwood paper drops to the very low

value of 0.0044 in about a week. Clearly, during the earlier times the paper is

reacting with the pollutant in solution in the paper and the much smaller

amount in the gas phase. The concentration decrease represents the fact that

diffusion through the wails of the container cannot keep up with the rate of

reaction and the concentration inside the container must necessarily drop, but

15
this takes longer for the less reactive paper. In this sense the reaction is

diffusion rate limited, but the diffusion is that through the wall of the

container and not into the documents . The final concentration for the more

reactive paper is lower than for the less reactive paper, which is what is to

be expected. These results show that sealed boxes can provide protection, a result that will become even more evident when the results for the

concentration of reacted species in the paper are discussed.

In contrast with these results are the results for boxes with gaps. These

are given in Fig. 8. Here the results are strikingly different. For the less

reactive pure rag paper, the concentration in the gas phase maintains its

initial value, which is the same as the exterior concentration. For the more

reactive groundwood paper, the concentration drops within one hour to a value

only about 0.93 of the exterior concentration. In both cases, diffusion through

the gaps just about keeps up with the rate of reaction. For all practical

purposes the box provides no protection from the pollutant.

These results are corroborated and made more meaningful when the

concentration of reacted material in the box contents is calculated. This is

given by Eq. 13, and is plotted in Figs. 9 and 10. Note that both these figures

are on a log-log scale to make the results more evident. Consider first Fig. 9,

which is for diffusion through walls. This figure contains two straight lines

which represent the situation when the documents are not in a container.

Consider now the case when the container holds the less reactive pure rag

paper. At first, for about a year, the change of concentration of reacted

material follows the curve for paper outside the box. Then the reaction rate

decreases and in about a 5 years becomes linear again, and the concentration of

reacted material is about 0.7 what it would have been in the absence of a container. Diffusion through the wails can just about keep up with the rate of

reaction. The behavior of the more reactive groundwood paper is the same, but

far more pronounced. Thus, for somewhat more than an hour, the change in

concentration of reacted material is the same as would occur in the absence of

a container, but then, in the period of about a year, the reaction drops and

eventually becomes linear again. However, recall that this is a log- log plot.

What this means is that the concentration in this case when it reaches the

steady state condition is less than 1/100 what it would have been in the

absence of a container, and remains so as time goes on. This, then, represents

the maximum protection that can be provided by a sealed box with the various

values of the parameters for box and contents we have chosen, and, of course,

based on our model. Diffusion through the walls can just about keep up with the

rate of reaction of the slowly reacting paper, but not with the fast. The

rather obvious conclusion is that if the diffusion constant or the solubility

coefficient for the walls were zero, then there would be no reaction after all

the pollutant in the gas phase and in solution in the contents was used up. The

formalism predicts this obvious result, but also gives what happens when this

limiting condition does not obtain.

Consider now what happens when there are gaps in the box. The results for

this case are given in Fig. 10. Here the curves are very simple. For both the

pure rag and the groundwood papers, they are essentially linear on the log- log

scale representation. Moreover, a comparison of these curves with the lines

representing the unboxed papers in Fig. 9 shows that the concentration of

16
reacted material in the contents of the box with gaps is essentially the same

as for the unboxed papers. We are forced to conclude from these results, and

from this rather simple model (which of course needs experimental verification)

that boxes with gaps of the size we have assumed provide little if any

protection from a reactive environment. The microenvironment is practically the

same as the ambient macroenvironment.

Having investigated the case with reactive contents for a constant

exterior concentration of pollutant, we now investigate the case of a fluctuating external concentration. This is carried out in Appendix A- 8, but

the exact solution (which could very likely be carried out by the methods in

Appendix A- 6, but would certainly be quite complex) is eschewed. The

approximate solution proceeds as in Appendix A-4, and the result is

= 1 - (1 - -t/r. . Cf 1 Sin(wt+5)

15

Again, because of the factor 1+w^r^, the sinusoidal term is negligible for the

case of diffusion through walls, and is present for the case of diffusion

through gaps. Moreover, in calculating the amount of reaction, this term causes

some analytical difficulties, hence this matter was not pursued. The conclusion

is the same as before: It adds a minor perturbation to the case of diffusion

through walls, and for the case of diffusion through gaps changes the

microenvironment somewhat, but not significantly.

2.6.1 Discussion and Conclusions

The most significant conclusion from this section is that containers can

provide protection from the macroenvironment, but provided they are sealed and

have no gaps in them. The reason for this is that the presence of reactive

material in the container substantially changes the environment inside the

container, and serves to reduce the level of pollutant inside the container.

The rate of reaction then becomes very strongly dependent upon the rate of

diffusion of pollutant through the walls of the container, and if this is low, so will be the reaction rate. The obvious conclusion, already mentioned, is

that if the diffusion constant is zero, i.e., if the container is hermetically

sealed, and the walls are impermeable, after a while reaction will cease. However, as will be seen later, other problems may arise.

The question naturally arises, ”What happens if the container wails react

with the pollutant?" This is perhaps the most important of ail the cases

studied, and will be taken up next.

2 . 7 The Container With Reactive Wails

2.7.1 Introduction

Having treated containers with inert contents and with reactive contents

this section investigates containers with reactive walls. Of the various cases

investigated, this one appears to be the most promising for the protection of

17
docuunents . The reason for this is easy to see. If the container reacts with the

pollutant as the pollutant diffuses through it, then the pollutant may never

get into the container, or perhaps only a small amount may get through,

depending on the extent of reaction. In due course, the container may be

destroyed, but the documents would have been protected. The container is

sacrificed to save the contents, much as is a sacrificial anode in corrosion

protection.

Indeed, this may already be the case with at least some of the NARA

containers. Archival storage boxes of the type we have chosen as the prototype

container for this report already are specified to contain 3% CaCOg (8)Every

person we have consulted on this project has remarked that SOg and NOg would

react with the CaCOg in their passage through the wails. Indeed, SO2 is known

to react with limestone, probably forming CaSO^ (17), and ozone would probably

react even with wail material that does not contain an additive. The. fate of

NO is not known, nor is the fate of other pollutants. However, it might be

hypothesized that acidic components that might be in the atmosphere might also

be removed by the CaCOg , and thus provide protection from these as well.

This section investigates two models of containers with reactive walls:

one an empty container, and the other a container with reactive contents.

Unfortunately, these are substantially more difficult problems than those

previously treated, so only a limited treatment can be given. However, even

this more limited treatment illustrates the principles involved.

In what follows, it is assumed that there are no gaps in the container

walls. Clearly, if the pollutant can diffuse or flow through gaps, then it

cannot react with the container walls. However, even in this case, the reactive

material of the walls may provide some protection. This will be discussed in

the discussion portion of this section.

2.7.2 The Empty Container

As already mentioned, the analysis of diffusion into a container with

reactive walls is a substantially more difficult problem than one with inert

walls. The reason for this is that there is an added term in the basic

diffusion equation, representing the fact that as a material diffuses it also

reacts. As before, it is assumed that this reaction is first order. This

somewhat simplifies the problem, but it is still difficult. Nevertheless, a formal exact solution is sketched out in Appendix A-9. The model is the same as in Appendix A-2, except that the pollutant now reacts with the wails with a first order reaction. The solution was not used because of the reasons

previously given, and is presented here because of the importance of the

problem, and because it might be used in future work. Even such a formal

solution does not appear to exist in the literature.

Appendix A- 10 gives an approximate solution to this case and to the case

of a container holding reactive documents. The approximation used here is more

restrictive than the one used previously of a linear concentration gradient. It

was felt that the use of that approximation with reaction as well as diffusion

taking place in the walls would not be realistic, so the problem was solved

only at steady state, i.e.

after sufficient time has passed that the system no

18
longer shows any time dependence. This approximation was previously used by

Odian and Kruse (18) in a somewhat simpler context, and corresponds to Eqs . 7 and 12 with the exponential term missing. For an empty container (or, as before, for one with inert contents) the solution for the fl^ix of pollutant

into the container is

F= SC,.C,S^osh ri

where all the terms have the same meaning as before and r is defined in

Appendix A-10. Now, by hypothesis, the exterior concentration,

2 , is constant,

and since this solution is for steady state, the interior concentration,

must also be constant. This can only happen if something inside the container

is consuming the pollutant at just the rate at which it is flowing into the

container, or if the flux into the container is zero. The latter is obviously

an important result, and the condition that it obtain is given by

= -csibi

This interesting result gives the relation between the interior and exterior

concentrations for the flux of pollutant into the container to be zero. Note

that the relation depends upon k, D, and 1. For a given value of the exterior

concentration, the interior concentration for zero flux into the empty

container decreases as k and i increase, and as D decreases. This is accord

with expectation.

What this relation means is as follows. At the interior boundary of the

container wall, pollutant will flow out of the wall and into the container.

However, pollutant will also diffuse into the wail from the atmosphere inside

the container. The relation gives the condition that these two flows be equal.

Table 5 gives some values of the ratio of Cj^/Cj for the prototype

container. Unfortunately we have no values of the rate constant k for paper

containing CaC03 , so we have used values calculated from the data of Hudson,

et.ai. (14-16). Recall that the lowest values of k were for rag paper, and that

the highest values were for paper containing groundwood. These calculations are obviously for illustrative purposes only, but the enormous range of values of

the concentration ratio should be noted. This comes about because of the

exponential character of the hyperbolic cosine. If these values are correct,

then it could be concluded that even boxes made out of groundwood would be

effective in protecting contents, but this would be a very bad error, for in

that case, other and serious complications arise.

2.7.3 The Container With Reactive Wails and Reactive Contents

This model is also solved in Appendix A-10. The result for the ratio of

the interior concentration to the exterior is

19
Cl 18 Vc k.

A rs^

C.

Sinh r^i + Cosh r^i

where and k^ are the reaction rate constants for the walls and the

constants, respectively, for they need not be constructed of the same

materials. Again, numerical results were calculated as in Sec. 2.6 for the same conditions as in that section and for the four possible combinations of the two

rate constants used there. Now, since the rate of reaction is proportional to

the concentration, this is the same as the ratio of the rate of reaction of

contents inside the box as compared to what it would be in the absence of a box. Hence, within the limitations of the model, it represents the degree of

protection provided by a box with reactive walls, and, of course, is the

microenvironment inside such a box. It is important to note that the results

are dependent upon both the walls and the contents. They act together. The

ratio for a box made of rag paper filled with rag paper contents is 0.09, while

for the groundwood-groundwood combination is a totally negligible 10"® Again,

this should not be read as meaning that archival boxes should be made of

groundwood, for then, as will be discussed later, other serious problems arise.

What the results indicate is that if the wails of the box are constructed of a material that has a rate constant for reaction with pollutant of the value we have chosen for groundwood and all other things are equal , then the protection,

again within the limitation of the model and the approximate nature of the

analysis, will be as indicated by the results in Table 6.

2.7.4 Discussion and Conclusions

This section has shown that a sealed box (no gaps) constructed of

reactive material can provide essentially complete protection from pollutants

provided that the box wails can react with the pollutant. Again, this is a rather obvious result, but the means for the calculation of the amount of

protection provided are given, at least for a simple case. The case with gaps merits some discussion. Generally speaking, gaps will

"short out" the wails and hence preclude the protection provided by the wails

if they are reactive, as in this model, or even if they are not, as in the

previous model. However, as pointed out to us by Professor Cass, this need not

be the case. If the gap has a long enough diffusion length, then as the

pollutant diffuses through the gap, it will also diffuse to the wails of the

container. There, if the walls are sufficiently reactive, it can react with

them and thereby be prevented from diffusing into the container. This

mechanisms merits further investigation.

2.8 The Book Problem

As mentioned in the Introduction, books are not generally stored in

containers, although they may be sealed in polyethylene shrink wrap, or they

may be stored in closed book shelves. Whether they are so stored, or are stored

on open shelves, there is a problem of the mechanism by which pollutant attacks

20
the book pages. The problem is simply stated: "Does the pollutant diffuse in

through the edge of the sheets or does if diffuse in between the sheets and

then spread laterally?" It will be clear that this applies to documents

contained in folders as well. It will also be clear that the looser the sheets

are packed, whether in a book or a folder, the more likely is diffusion to

occur between the sheets and then spread laterally, because the diffusion

constant in gases is so much greater than in solids. Because of its intrinsic

importance this problem was investigated.

The "book problem" is a problem of diffusion into a laminate composite,

but with diffusion occurring from the edge of the composite, not from the face,

as is usually considered. There are two published exact solutions for the

temperature distribution for heat flow from the edges of such composite

laminates (19,20), one for constant temperature boundary conditions, and the

other for time varying boundary conditions. Such heat flow problems can

generally be converted into diffiision problems, but this was not done in this

case because of the complexity of the solutions. Rather, a simpler approach was taken

There is a well known phenomenon in metallurgy known as "grain boundary

diffusion." The boundary between grains in a polycrystailine metal is known to

have a much higher diffusion constant than the region in the grains. Hence when

diffusion occurs in a polycrystailine metal, the diffusing material travels

down the grain boundary and then spreads laterally into the grain. This is

similar to the book problem, with the space between the sheets taking the place

of the grain boundary.

There are two well-known solutions of the grain boundary problem (21,22).

The first of these, by Fisher, is easier to apply and was the one used for this

report. Using the terminology for the book, it gives the ratio of the

concentration inside the book to the exterior concentration as a function of

the distance from the edge of the book sheets (y)and from the center of the

position between sheets (x)

The result is

with the following definitions:

7i= y/5(DVD)

S = Thickness of the inter- sheet region

D'= Diffusion constant in the inter- sheet region

D = Diffusion coefficient in the sheet

ti= Dt/S

x^= x/5

From this, knowing the values of the various constants, the concentration

profile for the pollutant within the book sheets can be calculated.

In order to apply this, the thickness of the inter-sheet region must be

known. This will, of course, be dependent on how much pressure is applied to

19

21
the book, or alternatively, how tightly the book is packed on shelves. To get

some idea of what this might be, a very rough experiment was carried out. Ten

books from the author's library were measured. The thickness of the sheets was

measured, and the thickness of the book was measured (excluding the covers)

using an eleventh book as a "standard weight". It was found that, on average,

the thickness of the book was approximately 10 % greater than the sum of the

measured thickness of the sheets, with values ranging from 6 % to 16%. Sheet

thicknesses varied from 0.0078 to 0.016 cm. These, of course, must be

considered to be very crude measurements

The most serious problem in carrying out a calculation is the value of

the inter- sheet diffusion constant, D' . It would be expected that its value

would be lower than the value for air and higher than the value for diffusion

in the sheet material, but where in this enormous range the value might

actually lie is hard to determine. Nevertheless, in the nature of an

exploratory calculation, its value was taken as that for diffusion in air,

namely 0.2 cm^/sec. The concentration profile was calculated for a diffusion

time of one day, with the following values of the other parameters: =0.001

cm; D=10"® cm^/sec; sheet thickness=0 .01 cm. The results are shown in Table 7,

which gives the concentration ratio as a function of the distance from the edge

of the sheets at the position between the sheets and at the center of the

sheets

The results are totally contrary to experience. They show that if the

diffusion constant in the inter-sheet region were that in the gas phase, after

only one day or so, the whole book would be permeated by pollutant. The brown

discoloration commonly observed around the edges of book sheets (increased by

lignin, hemicellulose , resin and and trace metal ion content of the paper(25)),

would instead be uniform over the sheet. To the extent that these very crude

results have any meaning, they indicate that the diffusion constant between

sheets is more nearly that for diffusion in the sheets than it for diffusion in

the gas phasa. The whole book acts almost like a block of solid paper. The

inter- sheet region is very likely a quite complicated thing, perhaps

corresponding to diffusion through a percolation maze.

On the other hand, the results do indicate that if sheets are loosely

packed, then the high diffusion constant in the gas phase assures that they

quickly become permeated with pollutant, an assumption that was used in some of

the models.

2.9 An Analysis of the Data of Hudson and Co-workers

In a series of three papers (14-16), Hudson and co-workers studied the

"uptake" (sorption) of SO2 by papers of various kinds. These workers found that

the sorption processes could be divided into two steps: a relatively rapid

process that lasted for 24-48 hours, in which it was hypothesized that the SO2 was going into solution in the paper fibers or adsorbed on the surface of other

substances present in the paper, and a much slower irreversible one in which

the SO2 was "fixed", presumably by conversion to SO3 and thence to sulfate ion.

This latter process continues indefinitely with a rate that is strongly

dependent on the type of paper. The rate was shown to be accurately linear for

periods of up to six months, and to be proportional to the square root of the

22
SOj concentration in the gas phase. The concentrations were 10 ppm and higher.

In the words of Edwards, et.al.,(15),

A detailed consideration of the processes that are likely to be

important in the sulfur dioxide-paper system show that the sulfur

dioxide present in the paper may be held in two ways, i.e.,

"reversibly" and "irreversibly".

The reversibly sorbed sulfur dioxide is in equilibrium with the

sulfur dioxide in the gas phase. It most probably corresponds to

sulfur dioxide "dissolved" in the cellulose/water matrix plus the

sulfur dioxide (or "sulfite" ions) physically sorbed at the

surfaces of the inorganic oxide fillers or other polar solids

present in the paper. It may be noted here that not only would this

equilibrium be attained in 24-48 hours but also that the total

quantity of sulfur dioxide sorbed in this way within such a short

period may well correspond to almost the total sulfur dioxide

content of the paper.

Only the irreversibly held sulfur dioxide would appear to be

important in the context of the build up of acid in the paper. It

probably corresponds to sulfate ions (i.e. the oxidation products

of sulfur dioxide or sulfite ions), and to sulfonic acids, the

latter associated with the lignin content of the paper.

These were the best papers found in the literature that permitted at

least a crude approximation to some of the constants necessary in the

calculation of numerical results from a model. What is necessary to know are

the solubility coefficient S, the diffusion constant D, and the reaction rate

constant, k.

The first of these is easily obtained from the results at short times

(24-48 hours) . From the results as quoted, this corresponds to the solution and

adsorption of SO2

. In the first of the three papers, results are given for two

papers: a gelatine sized pure rag paper, and a rosin sized paper containing 60%

groundwood and 40% chemical wood. For both papers, the amount of this

reversibly sorbed SOj depended strongly on the relative humidity, with the

sorption-Rh curve having a shape similar to the moisture regain curve. At 50%

Rh, the sorption was about 200 ppm for the rag paper, and about 300 ppm for the

other paper. In both cases the gas concentration was 10 ppm, so the values of S are 20 and 30, respectively. The value of 30 was used in the calculations. It

should be mentioned that it was assumed that the units of "ppm" were the same

in the solid as in the gas phase. The question of the solubility coefficient

will be returned to at the end of this section.

The determination of the diffusion constant is equally straight forward,

but an important assumption is necessary. As seen in Appendix A-9, the solution

of time dependent problems in diffusion with reaction are difficult. Moreover,

the actual curves of amount sorbed vs. time would have to be available for

analysis, and these were not. Hence it was assumed that in these short times

sorption takes place with a negligible amount of reaction, an assumption that

appears to be justified by the data (15). Then the calculation of the range of

diffusion constants consistent with the results is a standard problem (5)

Ail

that is necessary is the thickness of the sheet, which may be calculated from

23
the basis weight (14). From such a calculation it was found that diffusion

constants of 10"® and 10"® cm^/sec were consistent with sorption in 24-48

hours, but 10"^ cm^/sec was too fast and 10"^® cm^ was too slow. Hence the

values that were used in the illustrative calculations.

The calculation of the reaction rate constant, assuming a first order

reaction, presents considerably greater problems. As seen in Appendix A-9, the

full time dependent solution becomes quite difficult, so only the steady- state

solution was used. This is given in Appendix A-11. This shows that at steady

state, the slope, m, of the pollutant concentration vs. time curve is given by

m

C,k

i

D

k

tanh 20

where is the surface concentration in the sheet. In this particular case,

where the results indicate that diffusion is not the rate limiting stfep, may

be identified with the concentration after the first reversible sorption has

taken place. Moreover, the values of m are known. They are given as follows

(15), in parts/lO^/day : two rag papers with m=0.099 and 0.058; a group of nine

papers of various types with an average m of 0.5; and a newsprint of 80%

groundwood and 20% chemical wood with m=3.46. Then, knowing ail the quantities

save k, Eq. 20 may be solved for the latter by numerical iteration techniques.

However, since all the values of C, were not available for all cases,

calculations were carried out for a range of values taken from the data for

this quantity, as well as for the two values of D found to be consistent with

the data as discussed above.

When the calculations were carried out, it was found that kC3 /m=l. It can

be shown (18) that this indicates that the concentration of unreacted pollutant

in the sheet is uniform, which is consistent with the reaction not being

limited by diffusion, which in turn is consistent with the experimental

results. The results are shown in Table 8. The two extreme values of k,

2.9x10"® and 830x10"® sec" ^ , for the least reactive rag paper and for

newsprint, respectively, are the two values used for illustrative calculations.

We now return to the question of S and to a fact that was mentioned above

but was not discussed. This is the fact that the rate of the slow, fixation

reaction was determined to be proportional to the square root of the

concentration in the gas phase (15). The most reasonable explanation of this is

that the concentration of unreacted SO2 in the paper is also dependent on the

square root of the concentration of SO2 in the gas phase, i.e., the sorption

isotherm is not linear, as we have assumed. These experiments were carried out

at gas phase concentrations greater than 10 ppm, which is quite high- -perhaps

by a factor of over 100- -for the concentration of pollutant found in air under

normal conditions, a factor mentioned by the authors (15). It is not known if

this square-root proportionality holds down to the usual air pollutant

concentrations. If it does, the assumption that S is independent of the

concentration, made for mathematical expediency, is not correct. However, it is

felt that the qualitative nature of the results would not be changed, nor

would the general conclusions.

2.10 Models Not Solved

24
There is a class of important models that we have not yet considered.

These are models when the container holds tightly packed contents, so that

diffusion into the contents as well as through the walls of the container is an important, rate limiting process. When we did consider the contents, they were

either inert, or were loosely packed so that diffusion into them was not a rate

limiting process. When this is not the case, the problem becomes one of two

separate diffusion problems, but coupled through their boundary conditions.

These are very difficult problems to treat analytically and are probably best

handled experimentally.

2.11 Sealed, Impermeable Containers; Encapsulation

As has been seen from the analysis of the various models, and is obvious

a priori , if record documents are placed in sealed containers impermeable to

pollutant, then they are protected from the pollutant. The worst that can

happen is that they react with the pollutant trapped in the atmosphere of the

container or in solution in themselves at the time of sealing, and re- introduced when the docioments are removed during normal usage. (This does not

mean that the documents will not degrade, as will be discussed later in the

report.) The question then naturally arises, "Why not store records in sealed,

impermeable containers?"

There is, in fact, precedent for doing this with some types of records.

Thus, ANSI standards PH 1.48-1982, "Practice for Storage of Black- and- White

Photographic Paper Prints", and PH 1.43-1985, "Processed Safety Film Storage",

both recommend sealed, impermeable containers ("enclosures" in the terminology

of the standards) for the archival storage of the subject records. Archival

storage conditions, defined for safety film, but presumably the same for paper

prints, are, "...those that are suitable for the preservation of photographic

film having permanent historical value." Why is this not recommended in cases

other than safety film and photographic prints?

The answer is found in the standard for safety film itself. Sealed

containers are not recommended for cellulose nitrate based films, for these are inherently unstable and degrade and give acidic degradation products. In the

case of paper, Dr. Charleton Bard (26), noted that photographic paper is pure

alpha-cellulose, which is highly resistant to degradation and gives off no degradation products. With other, more degradable papers, sealing in a container may actually be worse than storing in the open, for the degradation

products serve to increase the rate of degradation of themselves and perhaps

other, less degradable, papers in the same container in an auto -catalytic

manner. As will be discussed in a later section of the report, one of the

principal reactions involved in the degradation of paper is hydrolysis. This

reaction is catalyzed by acids, and since there are acidic degradation

products, these further catalyze the degradation reaction. The harmful effect

of a pollutant like SOj is not necessarily to react with the cellulose molecule

but rather to be converted to SO3 and hence sulfuric acid, which catalyzes the

degradation. Paper at a normal regain contains approximately 4% water, which is an enormous reservoir of water available for hydrolysis.

Indeed, it was the opinion of all the experts consulted that, unless the

paper is of high quality and resistant to degradation, sealing (or

25
encapsulation) may actually be harmful, except, of course, for physical

protection. Moreover, sealing good paper in a container along with bad paper

may be harmful to the good paper. Also, the inclusion in the container of

unstable substances like nitrocellulose also promotes the degradation of the

other records.

While this is the feeling of the experts based on their long experience

and is undoubtedly correct, direct laboratory evidence that sealing in

containers is harmful is scanty. At this point it is helpful to define our

terms a bit more precisely. By sealed containers we mean those that have no gaps as described in the section on the prototype container. By impermeable

containers we mean sealed containers constructed of a material impermeable to

the pollutant or other substance in question, i.e., where the solubility and/or

the diffusion constant are zero. Such materials are aluminum, stainless steel,

etc., and are specifically referenced in PH 1.48-82. By these definitions,

encapsulation of a document between, e.g., polyester sheets, is not the same as placing it in an impermeable container, for the pollutant can diffuse through

the sheets. Encapsulation is, indeed, the same as the model in Sec. 2.6, but

without gaps, and, of course different dimensions and other parameters than the

ones chosen for illustrative purposes.

We know of only two laboratory experiments that deal with the comparison

of the degradation rate of paper in sealed or impermeable containers with the

rate without containers but otherwise comparable conditions (27,28). The first

of these was concerned with the degradation of Whatman papers in sealed glass

tubes at lOOC and a calculated Rh of 42% as compared to degradation at the same temperature and Rh an oven. It was found that the degradation rate, as measured

by changes in reflectivity and the degree of polymerization, was greater in the

closed tubes than in the oven. It should be noted, however, that this

experiment does not necessarily mean that degradation was hastened by

degradation products. The pressure -- particularly the oxygen pressure -- is

greater in the tube than in the oven, and this could be the cause of the

greater rate of degradation. The greater pressure is, in fact, the mechanism

espoused by the authors.

The experiments by Shahani (28) are similar, but with distinct

differences. Only the referenced letter and a personal conversation are

available to us now; the work is still in progress. In this work, paper was

encapsulated in polyester sheets, without holes and with holes to permit the

escape of acidic degradation products, if any. The important results of this

work are that for acidic or neutral papers, degradation inside the polyester

envelope, with or without holes, is faster than it is without encapsulation.

Most important is the effect of introducing paper with an alkaline reserve into

the envelope. In the author's own words, "The acceleration in the decline of

physical properties of acidic and neutral samples upon encapsulation can be

eliminated by enclosing another sheet of paper containing an alkaline reserve

in the same envelope." This very important result strongly indicates that

whatever degradation accelerating substances are released by the degrading

paper, they are probably acidic and perhaps are transmitted via the gas phase.

What these substances actually are appears to be unknown.

2.12 Recesses

26
So far we have been concerned principally with containers. These,

however, are not the only cases in which microenvironments may be established.

There are numerous regions or spaces, e.g., an empty shelf, or the region over

the tops of books packed on shelves (see figures on p.4 and p.l7 in Ref. 4) that

have limited access to the ambient stack environment. These spaces, which we shall henceforth refer to as "recesses”, provide for the possibility of a microenvironment, and, as with containers, we wish to determine how different

this microenvironment is from the macroenvironment of the stacks proper.

In many- -perhaps most- -cases, these recesses can be considered to be a rectangular parallelipiped open on one side to the ambient stack atmosphere,

and with the other five sides consisting of impermeable material. In cross

section, then, the recess can be represented by Fig. 2, but without the

membrane barrier. Now, it is clear that the slowest mode by which the recess

can exchange pollutant with the main stack atmosphere is diffusion. Any

convection that may take place can only hasten the exchange. Hence we

investigate diffusion into such a recess.

For this purpose, imagine such a rectangular recess with dimensions a,b,

and c, in, respectively, the x,y, and z directions. One of the faces normal to

the X direction is open; all other faces are made of impermeable material

(e.g., steel shelving). We consider only the simplest situation. Other more

complicated situations are easily handled, at least formally, but without

adding any new insight. We imagine that the environment inside the recess is in

equilibrium with the exterior environment, and, since the recess is open to the

exterior, this means that the two environments are the same. We now make a sudden change in the pollutant concentration of the exterior environment and

ask what happens to the concentration in the recess.

This is a standard problem in diffusion and heat flow. It is readily

solved, and bhe solution will not be presented. Only the results will be given.

What happens in this situation is that the change in concentration spreads into

the recess, but the concentration in the spreading front is independent of the

y and z coordinates. It is dependent only on the distance from the open edge of

the recess, i.e.

depends only on the x coordinate. What this means is that the

rate at which pollutant spreads into the recess is independent of the lateral

dimensions of the recess . Our task, then, is simply to choose a position in the

recess and calculate the composition at that point as a function of time.

For purposes of illustration, a recess one meter deep was chosen and the

composition at the end of the recess opposite the open end was calculated as a function of time. The diffusion coefficient, as in the previous calculations,

was taken to be 0.2 cm^/sec. The results for the ratio of the concentration to

the exterior are as follows: after one hour, 0.018; after 12 hours, 0.85; and

after 24 hours, 0.98. It is thus seen, that after 12 hours the environment

inside the recess is essentially the same as the ambient environment. Any

convection that may be present will hasten the attainment of equilibrium. Since

12 hours is a short time compared to the degradation processes of concern, we conclude that for all practical purposes the microenvironment in a recess of

this depth will be essentially the same as the macroenvironment.

27
2.13 Cone lus ions

This concludes the portion of the report on models. There are several

conclusions that can be drawn from the analysis and that are very likely

independent of the assumptions made in it.

1) The microenvironment inside a container communicates with the

macroenvironment outside it by diffusion through the walls of the

container; by diffusion through any gaps or openings in those walls; or by pressure or temperature changes if there are gaps in the walls.

2) For an empty container with inert wails, the interior microenvironment

eventually becomes the same as the macroenvironment if the latter is

constant, or its average if it is fluctuating. If there are any gaps in

the walls, the interior environment is always very nearly the same as the

exterior environment, and follows any changes in the latter with only a small time delay. The time constant, or "relaxation time", for any

changes in the microenvironment in the absence of gaps in the walls is

given by Vi/ADS, and hence depends on the design of the container through

V,A, and i, and on the materials of construction through D and S. If

there are any gaps the expression for the relaxation time is the same but

without S, and its value is very small compared to diffusion through the

walls.

3) Presure and temperature cycles, for the ranges of change and time

scales assumed for those changes, are about as effective as diffusion

through walls in providing communication between the inside and outside

of containers.

4) If the container holds reactive contents, i.e., the contents react

with the pollutant (s) in question, then, in the absence of gaps in the

wails, the microenvironment inside the container can be substantially

different and more benign than the macroenvironment outside it. If gaps

are present, then the microenvironment can be the same as the

macroenvironment

5) If the container walls can react with the pollutant(s) in its (their)

passage through them, then essentially complete protection from the

pollutant can be provided. This may even hold if there are gaps in the

walls, provided the gaps are long and narrow.

6) The diffusion constant for the interface between sheets in a book is

much lower than for diffusion in a gas, and may approach the diffusion

constant in the solid phase.

7) Sealed, impermeable containers will obviously prevent any

communication between the inside and outside of the container and hence

provide complete protection from the exterior pollutants. However, if the

contents are reactive, they may may give off degradation products that

catalyze further degradation. (The contents "stew in their own juices").

The option of sealed, impermeable containers is limited to such items as

28
very high quality paper, safety film, and perhaps magnetic recording

tapes

8) Unless recesses are very deep, the microenvironment in them is

essentially the same as the macroenvironment.

9) There is a very limited availability of data in the literature with

which to make calculations from the models and to check them.

3. DEGRADATION AND ITS PREDICTION; DATA AVAILABILITY

3 . 1 Introduction

In this section we discuss the degradation of record materials and the

prediction of permanence by laboratory tests--the so-called study of

accelerated aging. These are very old and extensive subjects with an immense

literature, and reviewing all of it would far exceed the scope of this project.

Nor is such a full review necessary. In this report we are interested in

degradation caused by air pollutants, and, even more specifically, how the

microenvironment in containers may alleviate degradation. This considerably

narrows the scope. Moreover, not all record materials need equal attention. Of

the four principal record materials -- paper, photographic media, magnetic

media, and optical disks -- the last two are not presently suitable for

archival storage, perhaps as much for hardware reasons as for the inherent

stability of the materials themselves (4). In comparison to paper, the ability

to predict permanence, and the resulting standards for archival storage, are more advanced for other materials than for paper (4,29,30,31). Hence our main

emphasis will be on paper.

Recalling that this report is concerned with laying out a program for the

study of microenvironments and their consequences for protection from

degradation,” we shall also review the availability of data to permit the

determination of microenvironments.

3 . 2 Paper Degradation

3.2.1 General Review

The degradation of paper is a subject that has been studied for a very

long time indeed, and on which there is an extensive literature. Fortunately

there are a number of recent reviews (32,33,34) which give references to other

reviews as well as original literature. We obviously cannot write yet another

review of paper degradation, and hence we will summarize the elements that are important for our purposes. These are,

1) There are a number of measures of degradation and the quantitative

relationship between them is not always clear. These measures may be

classified into two broad categories which may be called "chemical

measures" and "physical measures". The chemical measures are those that

deal with chemical changes that occur in the paper substance on

degradation. These are (33)

decrease in the degree of polymerization;

increase in acidity; increase in carboxyl, aldehyde, ketone, and peroxide

29
content; changes in moisture regain; and changes in alkali solubility.

The physical measures refer to changes in those physical properties that

are of direct importance for the utility and use of the document. These

are: decreases in fold endurance, tear strength, burst strength, and

tensile strength; changes in elongation, modulus, tensile energy

absorption, wet tensile strength, and changes in blue reflectance. To

these should be added deterioration of image quality, but, of course,

this is determined by degradation of the ink, not necessarily only the

paper.

2) The single most important factor in determining the permanence of

paper is its acidity. Papers with low Ph degrade seriously. Those with

neutral or higher Ph (but not too high, for too high an alkalinity also

leads to degradation) are relatively stable. For this reason, calcium or magnesium carbonates are added to papers to increase their stability.

Standards for paper composition relating to their permanence are

available (35,36).

3) The principal basic chemical reactions that occur in paper degradation

are hydrolysis, oxidation, cross-linking, and thermal decomposition.

Changes in bonding are listed here by Wilson and Parks (33)but this

would not appear to be a basic reaction, but rather the result of one or more of them. Hydrolysis is the most important of these reactions, and

since it is catalyzed by both acids and bases, the reason for keeping

paper neutral or slightly basic is clear. Oxidation is catalyzed by

transition metals (Fe,Cu,Mn).

4) Only a qualitative relationship between the basic reactions and either

the chemical or physical measures of degradation is known. While it may

be difficult, if not actually impossible, to relate the basic reactions

quantitatively to the physical measures of degradation, it should be

possible at least in principle to do this for the chemical measures.

5) As already mentioned above in Sec. 2.10, degradation products,

presumably because they are acidic, catalyze the degradation of paper,

leading to an autocatalytic degradation process unless these products are removed or neutralized. There is evidence that hemicelluloses are

important contributors to this process (37).

The reason for re-stating these well-known facts is that we wish to put the

action of pollutants into context. We now proceed to summarize what is known

about the action of pollutants.

3.2.2 Sulfur Dioxide

The effect of sulfur dioxide on the degradation of paper and hence record

docijments has been studied for a very long time, and is the most studied of all

the pollutants. An excellent account of early work is given by Kimberley and

Scribner (38). Sulfur dioxide increases the rate of degradation of paper

substantially, but it does not react with the cellulose molecule directly.

Rather, it is converted to SO3 (or sulfate) as already discussed in Sec. 2. 8 , which increases the acidity of the paper and hence the rate of hydrolysis. In

30
a readable, concise and prescient account of the requirements for enhanced

degradation of library materials, Langwell (39) writes as follows:

Analysis has brought to light some interesting facts which

help in reaching an understanding of the mechanism of the reaction.

In the first place books containing paper made before about 1750

may have the outer binding completely destroyed by atmospheric

pollution and yet preserve the original strength of the paper

almost unimpaired, since paper made before 1750 may contain very

little metallic impurity. This suggests one process by which

atmospheric sulphur dioxide can be changed to sulphuric acid in the

paper, if it is assumed, as one has every reason to do, that the

metallic impurity accelerates the conversion of sulphur dioxide to

sulphuric acid. Laboratory experiments confirm this supposition,

and show clearly that the presence of moisture is also necessary.

A third factor which can be inferred from a consideration of

the extreme dilution of the sulphur dioxide in normal air is the

movement of the air; obviously sulphur dioxide cannot damage paper

unless a sufficient amount of it can make contact with the paper.

The essential factors are therefore; the amount of sulphur dioxide

in the air; the amount of moisture in the air and the movement of

the air. In the complete absence of any one of these factors paper

cannot accumulate appreciable amounts of sulphuric acid, and would

presumably last indefinitely. This is the modem theory of

permanence

He goes on to write;

From these observations the remedies for impermanence should depend

on:

1) Treating paper so as to remove the metallic impurity.

2) Treating the air to remove either the sulphur dioxide or all the

moisture; the latter is neither practicable nor desirable.

3) Restricting the amount of air which is allowed to circulate

round the books or paper.

That metals are important for the conversion of SO2 to SO3 (or sulfate)

is borne out by the work of Hudson, et.al.(16), who found that the rate of

"fixation" of SO2 was increased by raising the copper or manganese content of

the paper. Both these metals were more effective than iron. These workers also

point out that sulfonation of lignin can also take place, which may account in

part for the higher rate of fixation of SO2 by papers containing groundwood.

That acidification and subsequent degradation by hydrolysis is the

mechanism by which SO2 degrades paper is borne out by studies by Hudson (40) of

the surface acidity of pages in 25 old books. Copies of these books were

obtained from two libraries: one located in a rural environment and one in the

polluted atmosphere of Manchester, England. He found that the book pages were

higher in acidity near the edges, and higher for the books stored in the urban

than for those in the rural atmosphere. The more acid books showed more

degradation. These data were subjected to a statistical analysis by Baer and

Berman (41) with the following conclusions:

31
... to the degree that the variance in the contact pH for the two

groups of books studied by Hudson can be attributed to library

location and position on the page, the low pH at the edges of the

page as compared to the center of the page may be attributed with

great confidence to the differing conditions of storage for the two

libraries. It should be noted that environmental factors in

addition to the local SO2 concentrations, e.g., average annual

rainfall, frequency of use, maintenance practices, may have

contributed to the observed differences.

From these and other studies (1,4,33) it may be concluded that the

mechanism by which SO2 degrades paper is by its conversion to SO3 and hence

sulfuric acid, and the subsequent acid catalyzed hydrolysis of the cellulose

molecule and other components in the paper.

3.2.3 Oxides of Nitrogen

In contrast to the situation with SO2 , work on the degradation of paper

by the oxides of nitrogen is very scarce. Certainly it is known that the

cellulose molecule is oxidized by N2 O4 to form primarily a carboxyl at the C -6

position and secondarily aldehyde and ketone groups at other positions in the

molecule (42)Other polymers are known to undergo chain scission by NOj

(43,44), but the only work that we have found that relates to the degradation

of paper is a study of the degradation of cotton fabric (45)

In this work,

cotton fabric was exposed at room temperature and normal humidity to

atmospheres separately containing various concentrations of NO2 and HCl, up to

6 % v/v. The results are somewhat puzzling. Thus, HCl causes greater

degradation in tensile strength than does NO2 , but both show the same changes

in fluidity in cuprammonium solution, and hence presiimably comparable changes

in degree of polymerization. Moreover, NO2 causes large changes in carboxyl

content, while HCl causes none, and larger changes in copper number than does

HCl. These results imply that NO2 causes about the same amount of hydrolysis

(decrease in the degree of polymerization) as does HCl, plus some oxidation

that HCl does not produce , yet does not degrade tensile strength as much. This

puzzling result, along with the paucity of other work shows that this area is

greatly in need of work if the effect of on paper is to be understood.

3.2.4 Ozone and Other Pollutants

Ozone concentrations in the National Archives Building, at least in

winter, are at undetectably low levels (2). Their summer levels are unknown,

but data from libraries and museioms in other places imply that they might be

high (4,p.20). What the level is inside containers is also unknown, but one can hypothesize that it would be low, even for containers with gaps (provided

they are long and narrow) , for such a reactive molecule would have trouble

getting into a container without reacting with the walls

Whatever the case, the action of ozone on paper is very little studied.

Bogarty, et.al. (46) showed that ozone in concentrations found in polluted air

(<0.06 ppm) degraded cotton when wet but not when dry, although the exposures

were only of thirty days duration- -hardly archival times. These studies appear

32
to be borne out by those of Morris (4,p.l8). There is clearly a paucity of data

on the effect of ozone on paper.

There are a number of air pollutants found in outdoor air that are potentially detrimental to paper (and other record materials) (4, p.l3), and

still more found in the indoor air of libraries and museums (1). Among the

latter are formaldehyde, organic acids, and oxides of nitrogen, the last given

off by materials containing cellulose nitrate, such as book bindings containing

pyroxylin. With the slight exception of NO2 , none of these has been studied,

although since many of them are acidic, the presumption is that they are harmful

3 . 3 Leather

Somewhat out of place we discuss leather. This is a special case. Many

books in the Archives are bound in leather, and they are not in containers.

Some of the bindings show signs of severe degradation. However, the degradation

of the bindings does not necessarily mean a similar degradation of the pages

inside the book, although this might be hastened by the lack of a container. If

the bindings do not have an intrinsic value, the book can always be re-bound,

which, however, is an added expense.

As with paper, the main degradation caused by air pollutants is via the

acidity caused by SOj , which is added to the normal acidity resulting from the

processing (1,34). With respect to other pollutants, there is the same paucity

of data as for paper. It is possible that the degradation of leather may lead

to the formation of volatile acids and hence an increase in their concentration

in the ambient stack environment, a variant of the situation in impermeable

containers discussed in Sec. 2.10. There appear to be no data on this effect,

if indeed it exists.

3.4 Lifetime- Prediction; Accelerated Aging

3.4.1 General

One of the principal goals of materials science and engineering has

always been the prediction by laboratory tests of the lifetime in service of

materials and structures. The ability to predict the life of an object before

that object is put into service can lead to the use of proper materials and

design and hence prevent unanticipated failures with a consequent saving of

human and capital resources, the preservation of objects of social and cultural

value, and, often, the saving of human life. Thus it is hardly surprising that

the study of the laboratory prediction of lifetime in service of record

materials has been a long and continuing effort. Here we discuss paper.

An excellent review of these efforts is given by Roberson (47)

who also

lists other reviews, and there are a number of other papers (37,48-55) that

bear on important aspects of the subject. As before, we cannot review all this

work, and will only discuss those features that are important for our purposes.

Briefly, then, in these studies advantage is taken of the fact that

temperature increases the rate of chemical reactions . A measure of degradation

33
is chosen and measured as a function of time of exposure of a sample to a temperature that is high enough that the work can be carried out in a reasonable time. This gives the rate of degradation according to that measure

as function of temperature. This is not always simple to do because plots of

the measure against time are not always linear (51,53), but this can sometimes

be remedied by different handling of the data (52) or by other semi-empirical

methods (53). Whatever is done, a rate constant is determined at different

temperatures. An Arrhenius plot of all these is made. This is used to

extrapolate to room temperature, and hence a degradation rate at room

temperature is obtained. The most common measures used are one or more of the

physical measures discussed in Sec.3.2.1, most commonly fold endurance and blue

reflectance. In special cases when the data are available, the results of

accelerated tests may be compared and correlated with many years of natural

aging (49,40). With some measures and with some papers, good correlation exists

(49), and then accelerated aging can become lifetime prediction.

Then a statement like, "Forty eight hours at lOOC is equivalent to 13 years of

natural aging" can be made, but the correlation is totally empirical, and does

not necessarily hold out of the context in which it was derived. Nevertheless,

two useful standards (56,57) to give a relative estimate of permanence have

been developed on this basis. These involve heating papers for 72 hours at

105C, and the fold endurance measured. With the proviso that "It has not been

established that this test method is suitable for papers with a high groundwood

content, and no evidence is available of its being satisfactory for coated

paper or for those containing wet-strength resins", the ASTM standard goes on

to state.

The heating condition specified in this test method produces the

deteriorative reactions, excepting photochemical, of the normal

components of papers similar to those occurring on long aging of

paper in air at room temperature. It is recognized that heating

paper under the conditions specified is not a normal treatment

which the paper would receive in use, but research has indicated

that the results of heating under the prescribed conditions

correlate with those of normal aging. The effect as measured by

this method is approximately equivalent to that of normal aging for

25 to 28 years.

While this approach can give a relative ranking of papers, it is

recognized that there are deficiencies in it (47,53,54,55). First, for it to be

useful, the Arrhenius plots for various papers must be linear and parallel . otherwise individual plots would have to be made for each paper (53). Second,

and perhaps most important, it is almost axiomatic in lifetime prediction that

the basic reactions that affect degradation and their relationship to the

measure of degradation must be known if accurate accelerated tests are to be

developed. In the particular case of paper, as discussed in Sec. 3.2.1,

permanence is usually defined on the basis of one or more of the physical

measures, whereas the basic reactions are hydrolysis, oxidation, crosslinking, bonding, thermal decomposition and perhaps others. The relationship of

these to the physical measures are not known in any detail. Thus, Browning (58)

writes

The changes in a paper property with time are not determined by any

34
single chemical reaction whose effects can be isolated and

controlled. Hence, applications of conventional kinetic treatment

to aging data on paper are largely empirical.

Third, there are the conditions of accelerated aging. In natural aging,

the paper is at customary relative humidity and hence contains several percent

water. However, when heated in an oven at 105C, as is done in the standard test

methods, the paper is desiccated. Indeed, the standards require that the paper

be desiccated before testing so as to approach its final condition from below.

It is well established that moisture content increases the rate of degradation

(54,55), whether achieved by enclosing samples in sealed tubes or placing them

in a humidity controlled high- temperature chamber, which is more difficult

experimentally. It would seem natural to use conditions such that the moisture

content under the test conditions are the same as in natural aging, including

cycling of temperature and humidity. Roberson writes (47):

Since the purpose of accelerated aging is to duplicate natural

aging chemically and physically, the degree to which this is

accomplished is the proper measure of a test method's validity. It

seems logical that moist aging with cycling of temperature and

humidity might do this better than dry- oven aging, but it has not

yet been demonstrated.

By the final comment he apparently means that no empirical correlation between

moist aging and natural aging has been made.

In this context we return to the subject of aging in sealed tubes. Such

studies were carried by Browning and Wink (53) as a substitute for the

experimentally more complicated moist high- temperature oven conditions. The

rate of degradation in these sealed tubes was about eleven times as fast as in

dry aging. Also, apparently reporting from work not available to us, Roberson

reports that degradation in sealed tubes occurred at the same rate as in moist

oven aging. This contrasts with the results of Santucci and Zappala-Plossi (27)

who found aging in tubes to be more rapid, a result that seems to us and to

Roberson to be more reasonable for the reasons discussed in Sec. 2.10.

Finally we should discuss cycling. In normal usage, both temperature and

humidity will not usually be constant, although they practically are in the

National Archives storage conditions. If the measure of degradation really

follows the Arrhenius equation, and the time- temperature variations are known,

then the effect of temperature is easily calculated by using an appropriately

weighted mean temperature. However, if relative humidity also changes, with the

consequent hysteresis effects this causes, then the problem becomes more

difficult. This problem of temperature cycling and humidity was investigated by

Cardwell (59) who reported that cycling between 105C, dry, and 23C, 50% Rh,

caused greater degradation than constant aging at 105C. His description of the

experiment is, however, not completely clear, and this merits further

investigation.

To summarize, accelerated aging to give a relative measure of .permanence

is both possible and useful. To make accelerated aging a more quantitative

predictive technique, relationships between the physical measures of aging and

35
the basic primary chemical changes that occur on aging need to be established.

Then with a knowledge of the activation energies of the basic chemical

reactions, there is at least a hope of putting accelerated aging on a fundamental, quantitative basis. Doing this is likely to be a long and

difficult task, but without it prediction of lifetime by accelerated aging will

remain a useful but empirical science.

3.4.2 Accelerated Aging and Pollutants

So far we have not said anything about pollutants. The reason for this is

simple; there is very little in the literature on accelerated testing for the

effect of pollutants. In work with SO2 , Kimberly (60) exposed several papers to

an atmosphere containing 1-9 ppm of SO2 for 240 hours at 30C and 65% relative

humidity. Fold endurance decreased considerably, acidity and copper number

increased (indicating hydrolysis), but tensile strength did not change. Since

the concentration of SO2 used was substantially higher than that found' in

normal usage, this can be considered an accelerated test. In a similar vein,

Edwards, et.al., (15), using their rates for SO2 sorption and conversion to

SO3 , as discussed in Sec. 2.8., were able to extrapolate their rates to a concentration of 0.1 ppm SO2 , which is approximately the concentration in

polluted atmospheres. From this they calculated that in 25 years book papers

would pick up about 0.7% SO3

. This agrees remarkably well with results by

Langwell (61) on actual books. Since the Edwards experiments were carried out

at higher concentrations (>10 ppm) and were for relatively short times, these

again can be considered accelerated aging experiments, although no measure of

degradation was determined. The acceleration results from an increase in the

SO2 concentration in the atmosphere, resulting in a higher sulfate content and

hence acidity and hence hydrolysis and degradation of the paper. How far this

can be carried is not known.

The work of Schreiber, et. ai. , (45) on the degradation of cotton by NO2 has already been discussed. Since the concentration of NO2 used was 6 %, this

was clearly accelerated aging. Similarly, the work by Jellinek, et.al.,

(43,44,62)on chain scission in nylon and chain scission and nitration in

polystyrene by NO2 using quite high pressures (0.05 to 60 cm Hg) might also be

considered accelerated aging, although it was not done for this purpose. Both

Hudson, et.al, and Jellinek, et.al.

carried out experiments at various

temperatures and were able to obtain activation energies. Another group of

workers (63) were actually concerned with accelerated aging of nylon and Kevlar

by smog and ozone, using tensile strength as the physical measure of

degradation. It was found that smog seriously degraded the tensile strength,

but ozone did not. The latter result is in sharp contrast with the results of

Jellinek and Chaudhuri (62) who, however, used degree of polymerization as the

measure of degradation. Finally, in two papers, Igarashi and DeVries (64,65)

investigated the effect of O3 , NO^j , SO2 , and u.v. radiation on nylon and

polyethylene, using tensile strength as the measure. When samples were exposed

under stress, the environmental factors increased degradation, but without

stress there was little or no increase.

These few papers, on materials which are of only marginal interest for

record materials, illustrate the state of knowledge about the effect of

environmental factors on the rate of degradation of record and container

36
construction materials. Clearly, a great deal of work needs to be done in this

field if accelerated aging by pollutants is to be understood and become a useful discipline.

3.5 Data Availability

In this final section of this part of the report, we examine the

availability of data. The data in question are data for diffusion constant,

solubility coefficient, and, what is more readily available because of its ease

of measurement, their product, or permeability, P. We shall also be concerned

with the reaction rate constant, k, as discussed above, as well as the reaction

involved. We limit ourselves to the action of pollutants.

Literature searches using the Chemical Abstracts data bases were

conducted. For SO2 , presumably because of the interest in permeation tubes,

there were relatively speaking quite a few publications, but not many of them

were concerned with materials of interest to us. For other pollutants there

were relatively few publications.

An excellent compilation of data on transport properties for SO2 in

various materials is that of Felder, et.al., ( 66 ). While this compilation is

for many polymers, the data for those likely to be of interest in this study

are given in Table 9. While this may seem like a lot of data, it should be

noted that they come from only five references. It should also be noted that

the units of S are different from those defined in Appendix A-1. To obtain

those, the values in Table 9 should be multiplied by 76. The wide variation of

results (note particularly those for polyethylene) from different laboratories

should be noted. There is only one result (of questionable validity) for paper,

and that only for the permeation coefficient. This was the main reason for

going through the analysis carried out in Sec. 2.9. It seems rather clear that

when experimental investigations are carried out, transport coefficients will

have to be measured on the actual materials being investigated.

No data on the reaction rate constant for SO2 were found other than those

discussed in Sec. 2.9.

For NO2 there only three papers that give results (43,44.62). The first

of these is for polystyrene, and the values are: D=2.5xl0“®; S=0,4

cm^ (STP)/cm^ . cmHg. Two rate constants can be determined, one for chain scission

and one for substitution- on the tertiary carbon on the main chain. These are,

respectively, 2.4x10"® sec"^ and approximately 1x10"^ sec"

at room

temperature. Rate constants for chain scission in nylon 66 for NO2 and O3 are also available (44,62). Again, if experimental investigations are carried out,

transport coefficients and reaction rate constants will have to be determined.

3.6 Conclusions

Finally we list a number of conclusions that can be derived from the

information presented in this section.

1. Degradation can be characterized by a niimber of chemical and physical

measurements. The chemical measures are closer to the basic chemical

37
reactions that occur on degradation, but the physical measures are more

closely related to the actual utility of record documents.

2. The relationship of the physical measures of degradation to the basic

chemical reactions that occur in degradation are known in only a qualitative way. To put accelerated aging on a firm basis, this

relationship should be determined insofar as possible. This is likely to

be a long and continuing task.

3 . The degradation products of paper and other record materials are known

or suspected to increase the rate of degradation, and hence to cause

degradation to be autocatalytic . What these degradation products are is

not known. It is suspected that in the case of paper they are acidic and

promote further degradation by hydrolysis. It is not known if they are gaseous and hence capable of transmission through the gas phase..

4. Sulfur dioxide in paper acts by conversion to SO3 , and thence to

sulfuric acid. The rate of this reaction is increased by heavy metal

ions. This increased acidity causes an increase in the rate of hydrolysis

and hence degradation of the paper. Its action on other record or container wall construction materials is not known. It may be inert in

some of them.

5. The reactions of NO2 with cellulose are rather well known, but their

relationship to the physical measures of degradation in paper are not.

Data on transport properties are not known to us

6 . The action of ozone on records has not been studied. It is known to

degrade cotton fabrics under certain circumstances, and to react with

cellulose, but its effect on the physical measures of degradation is not

well known.

7. The accelerated aging of paper without consideration of the action of

pollutants has been a study of long duration, and has resulted in two

useful standards. Two important questions remain: the effect of humidity,

and the effect of degradation products , which is clearly of central

importance if degradation in sealed containers is to be predicted.

8 . There are only a few experiments directed at the accelerated aging of

paper in the presence of pollutants, and none on other materials of

interest as either record or container wall materials. As a simple

example of the type of experiment that has not been done, consider the

following. The rate of reaction of a pollutant can be increased by

raising the concentration or by raising the temperature. However, raising

the temperature decreases the solubility, which decreases the rate of

reaction. Thus, the relative effects of temperature and solubility have

not been sorted out.

9. The availability of data on transport properties and reaction rate

constants is such that these will have to be determined on the actual materials

under investigation when experimental investigations are carried out.

38
4. A RESEARCH PROGRAM

4.1 Introduction

It is clear from the structure of this report, and is evident ^ initio,

that the problems of concern in this whole question of microenvironments fall

into two areas:

1, What are the microenvironments experienced by record documents?, and

2. Given an environment, micro or macro, how rapidly do documents

degrade?

The aspects of the environment that are of concern are temperature, relative

humidity, pollutant concentration, and the important question of the presence,

nature, and action of degradation products. The principal emphasis here is on

pollutants and degradation products. Logically, then, the research should

address these two areas. This follows the structure of the report, and since

conclusions were given at the end of the two main sections of the report, it is

necessary to develop a research program that answers the questions posed in

those summaries. Here we describe such a program.

4.2 Microenvironments

In this section of the report a number on models that relate the

microenvironment inside a container to the macroenvironment (and any changes in

it) outside it were developed. If (a significant "if") these models were known

to be correct, then a knowledge of the container dimensions, and the relevant

parameters D, S, and k for the various poliutant/container wall combinations

would permit the calculation of the microenvironment inside the container. But,

as detailed in Sec. 2, a number of approximations had to be made in the

development of the models, so their validity has to be checked. Hence an

experimental program, supported by theoretical analysis, to check out the

models should be considered. While this program might be called, "validation of

the models", it should be noted that a great deal of important information on

microenvironments will be developed, whatever its intent. Specifically the

following experimental investigations are suggested. This largely follows the

analysis in the previous text.

4.2.1 The Container with Inert Walls

This is the simplest of the investigations. While it is probably not

applicable to the paperboard container used as a prototype in the report for

illustrative purposes, since its walls are probably reactive, it is likely

applicable in other cases where the wall materials are inert. This, in turn, is

likely to occur only with SO2 , since, as was seen, NO2 and O3 are quite

reactive. The objective of the investigation is to determine, in this simplest

case, how the microenvironment inside the container is affected by changes in

the exterior macroenvironment. As far as is experimentally possible, actual

containers should be used. The effect of gaps should be studied, for, as was

seen in the development, they are likely to be very important, and the

39
"breathing" as well as the diffusion modes should be investigated. Experiments

with the container empty and filled with reactive doctaments should be carried

out.

As part of this investigation the coefficients D,S and k will have be

determined for the actual pollutants, wall materials and record materials

involved, for otherwise a purely empirical investigation with hardly any

opportunity for significant analysis will result. The important point to note

is that if the models are verified, or an applicable model is developed, then

it is only necessary to measure these coefficients to predict what would occur

in a new and untested situation.

It is possible to do at least a part of this investigation (e.g., the

empty container) without using a pollutant gas. This is strongly discouraged.

Even though it would then be possible to predict what would happen with a pollutant, assuming an applicable model is developed, it would probably not be

wise to proceed without actual experiments with pollutants. Moreover, it is

unnecessary to use non-pollutant materials. Sulfur dioxide with a convenient

radioactive isotope for analytical purposes would appear to be a natural

candidate as a pollutant gas.

4.2.2 The Container with Reactive Walls.

This is viewed as perhaps the most important investigation that can be

carried out. As noted in Sec. 2.7, if the pollutant cannot get through the

container wails, then the contents are obviously protected from them. The only

question that then arises is the effect of degradation products

An experimental program that investigates this question would go as follows. First, determine the diffusion and solubility coefficients, and the

reaction rate constant for one of the wail material/pollutant combinations. In

this case,' paperboard with and without CaCOj , and with and without lignin would

seem to be very appropriate, as would SO2 because of the ease of measurement

and because some measurements already exist in the literature (13-15). Then

experiments with an actual container to determine the interior microenvironment

as a function of the exterior macroenvironment could be carried out. In this

case the prototype container, or a similar one, would appear to be highly

appropriate. Experiments with and without contents should be carried out. The

effect of gaps should be investigated, especially the effect of their aspect

ratio, for as pointed out in the text, long narrow gaps might prevent the

entrance of pollutants if the wall material is sufficiently reactive.

A full analysis of the experimental results derived from these

investigations would very likely require a full solution of the time dependent

diffusion problem. (Recall that only the steady state case was used in this

report.) This solution was sketched out in Appendix A- 9. To apply it would

require more theoretical work. This would be desirable but not completely

essential. A great deal of progress could be made experimentally with good

experimental design and analysis.

This is deemed to be possibly one of the most rewarding of the

investigations that could be carried out.

40
4.2.3 Degradation Products ; Encapsulation

It follows from the discussion in Sec. 2.11 and Sec. 3.4 that if

degradation products are not given off, or they do not catalyze further

degradation, sealing docioments in impermeable containers protects' them from an

aggressive environment. If degradation products are given off and do promote

further degradation, then sealing documents in an impermeable container will

still protect them from exterior pollutants but might compound the degradation

problem by promoting degradation by the degradation products because these are now prevented from diffusing away from the dociiments. However, if these

products can be removed from the container by the wail material, either by

reaction with them , or because the products can diffuse through the walls , the

container will at least not worsen the situation. Note that neither of these

two kinds of container can prevent the degradation of inherently degradable

materials; the best they can do is not to aggravate the situation. There is no substitute for high quality record materials. The first case, in which the

products can react with the container walls, might apply to the CaCOg filled

paperboard container, while the second might apply to a polyethylene shrinkwrapped book, although in this case the shrink-wrap might not protect the book

from exterior pollutants. This latter situation is in fact a special case of

the situation in Sec. 4.2.1, except that here we are now concerned with

diffusion out of degradation products, and diffusion in of pollutants.

It is the opinion here that not much can be done on this problem until

the degradation products are identified. Are they organic acids, aldehydes,

ketones, nitrogen oxides, or what? Are they gaseous or not, and even if not, do

they exist in the vapor phase? How are they transferred from one document to

another? By diffusion on contact or by transfer via the gas phase?

It is felt that until these questions are answered, only empirical

progress can be made. While this could prove useful (see Ref. 28), it is felt

that modem analytical techniques like gas chromatography-mass spectrometry

provide an opportunity for the identification of these products. An

experimental program on their identification would appear to be very much in

order and would begin to answer the vexing questions about the nature and

likely effect of these products.

When considering an experimental program, it should be remembered that

the primary, and perhaps sole, interest here is on degradation products in the

gas phase, for only then is the microenvironment changed. Then the effect of

containers becomes relevant. It is interesting and important to know, for

example, that the C-6 carbon on cellulose is oxidized to a carboxyl on

degradation, but not relevant to the problem of microenvironments. Only if that

carboxyl is subsequently released as, say, formic acid does it affect the

microenvironment in the container and hence influence another piece of paper

remote from the one in which it originated. An experimental program of this

type should include paper of various types as well as leather, pyroxylin

containing book bindings, and other materials of interest. An obvious follow-up

study is the reaction of these products with wall materials and their diffusion

through them.

41
4.2.4 The Book Problem; Folders

The problem of the mechanism of entry of pollutants into book sheets was

discussed in Sec. 2.8. There, on the basis of a simple calculation, it was

concluded that the interface between sheets in a book is probably of a complex

nature with a diffusion constant that is much lower than for gases, but whose

magnitude is hard to estimate. Aside from a more thorough theoretical

investigation, no particular course of action suggests itself. Moreover, it is

not clear that an investigation of this problem would be very useful. It seems quite clear that the more tightly books and documents in folders are packed,

the more the center portions of the sheets would be protected. Their edges, in

the absence of a container, will always be exposed to the macroenvironment,

however tightly packed, and in a container, the problem becomes one of those

already discussed. As a result, no particular research program is suggested.

4.3 Degradation; Lifetime Prediction

4.3.1 Introduction

The studies described in the previous section can be relatively shortterm, since they have the well defined goal of validating and/or developing

microenvironment models, or, as in Sec. 4.2.3, of identifying degradation

products. When it comes to the problems of concern in this section, the

research tends to be longer range, with goals that, while capable of

definition, are not as easily capable of attainment. The problems can be

grouped into three categories: the relation of basic chemical degradation

reactions to physical measures of degradation; the chemical effect of

pollutants on record materials; and accelerated aging by pollutants. We will

take up each of these in turn.

4.3.2 Relation of Basic Reactions to Physical Measures of Degradation

As discussed above in Sec 3.2, this is an important area of research

since a knowledge of these relationships is necessary to put accelerated aging

on a sound fundamental quantitative basis. A research program in this area

would include the identification of the basic reactions involved, and the

measurement of their rates and activation energies. While difficult, this is

the easy part. The difficult part is relating these to the physical measures.

While, for example, a great deal of work has been done on the relationship

between tensile strength and degree of polymerization (73), a chemical measure

of degradation which can be in turn related to hydrolysis, very little has been

done on the relationship for the more commonly used measure of fold endurance.

This whole area merits attention, but it should be considered a long-range

continuing study rather than one with a specific end, except possibly in

specific cases.

It should be pointed out, however, that if research on the identification

of degradation products as in Sec. 4.2.3 is undertaken, it could be considered

part of this study as well, for it would go a long way toward identifying the

basic reactions and their mechanism.

4.3.3 Chemical Effects of Pollutants on Record Materials.

42
This study involves the reactions that occur between pollutants and

record materials as well as their rates and mechanisms. Again, this is

important for the prediction of lifetime in the presence of pollutants and for

the development of accelerated aging procedures

It will be noted, however, that a part of this information will have

been developed if the research programs described in Secs. 4.2.1 and 4,2.2 are pursued, for carrying out those programs involves the reaction rate constant of

pollutant with both wall and record materials. The present study could be

considered an extension of that work to more pollutant/material combinations,

and carried out in more depth.

4.3.4 Accelerated Aging by Pollutants.

As was seen in Sec. 3.4.2, very little work has been carried out on

accelerated aging in the presence of pollutants, yet it is an important area if

the effect of pollutants is to be known in a quantitative manner. As in the

development of all accelerated tests, the mechanisms and activation energies of

the various reactions should be determined, as well as, ideally, their

relationship to the physical measures of degradation. Some of this information

would have been developed if the work carried in the previous section and in

Secs. 4.2.1 and 4.2.2 is carried out. Nevertheless, to carry out such a program

properly will be a long effort, albeit a worthwhile one. However, it is also

possible to proceed more empirically. Thus, having chosen a record materialpollutant combination, the effects of concentration, temperature and hiomidity

could be investigated. The problem here would be in the relationship of the

results of such an investigation to performance in service. There really is no way to do this without a comparison of the experimental results to service

results as was done for paper (49,50). However, such an empirical study could

permit the relative ranking of pollutant/material combinations. The whole

question of ^sealed tube aging naturally arises in this study, for moisture will

have a profound effect, and such aging again brings up the question of

degradation products

4.4 Summary and Conclusions.

The research program laid out can be grouped into seven elements, which

may be listed as follows.

1. Microenvironment and reaction in a container with inert walls.

2. Microenvironment and reaction in a container with reactive walls.

3. Identification of degradation products.

4. The "Book Problem" and folders.

5. Relation of basic degradation reactions to physical measures of

degradation.

6. Chemical effects of pollutants on record materials.

43
4

7. Accelerated aging with pollutants.

This program would, in our view, go a long way toward carrying out the

recommendations of the NAS Committee (4)

and go beyond them in developing the

effect of pollutants on lifetime in service. Setting priorities among the

elements of such a program requires a set of criteria, and many different

orderings can be achieved depending on those criteria. Using the criteria of

relevance to the problem of microenvironments in containers and the probability

of achieving significant results we would place the elements of the program in

the following order : 2, 1,3, 7, 6, 5.

Element 4 is omitted for the reasons given in the previous section. Element 6

is low on the list because a lot of the information that would be developed in

this element would be developed in carrying out elements 1 and 2. Element 5 is

low on the list despite its importance because it should really be considered

to be a continuing background research effort and probably would have only

long-term impact. Elements 1 and 2 are obviously central to the problem of

containers and their utility, and element 3 is central to the problem of

sealed, impermeable containers. Element 7 is placed where it is because of the

importance of predicting performance in service in the presence of pollutants.

Finally, it should be realized that this is a subjective listing based upon one set of criteria. Other criteria would very likely lead to another ordering.

Indeed, depending on resource availability and priorities, some elements can be

omitted entirely.

Acknowledgements

The author is pleased to acknowledge gracious, courteous and uniformly

helpful discussions with Professor Norbert Baer, Professor Glen Cass, Mr. Peter

Waters, Dr. Charleton Bard, Dr. Chandru Shahani, Mr. W.K. Wilson, Dr. Leslie

Smith, and Dr. Alan Calmes and the rest of the NARA staff.

44
REFERENCES

1. N.S. Baer and P.N. Banks, "Indoor Air Pollution: Effects on Cultural

and Historic Materials", Int. J. Museum Mgmnt. and Curatorship 4, 9-

20(1985)

2. E.E. Hughes and R. Myers, "Measurement of the Concentration on Sulfur

Dioxide, Nitrogen Oxides, and Ozone in the National Archives Building",

1983, NBSIR 83-2767, National Bureau of Standards, Gaithersburg, MD.

3. R.G. Mathey, T.K. Fasison and S. Silberstein, "Air Quality Criteria

for Storage of Paper-Based Archival Records" , 1983 , NBSIR 83-2795,

National Bureau of Standards, Gaithersburg, MD.

4. "Preservation of Historical Records", National Academy Press,

Washington, DC, 1986.

5. W.W. Nazaroff and G.R. Cass, "Mathematical Modeling of Chemically

Reactive Pollutants in Indoor Air", Env. Sci. and Technology 20, 924-

934(1986).

6. G.J.M. M®Rae, W.R. Goodin and J.H. Seinfeld, "Numerical Solution of

Atmospheric Diffusion Equations for Chemically Reacting Flows", J. Comp.

Phys. ^5 , 1-42(1982).

7. T.R. Young and J.P. Boris, "A numerical Technique for Solving Stiff

Ordinary Differential Equations Associated with the Chemical Kinetics of

Reactive-Flow Problems", J. Phys. Chem. 2424-2427(1977).

8. National Archives and Records Administration Specification (Revised

April, 1987); Boxes: Archival, Low Lignin, Metal Edged.

9. W. Jost, "Diffusion", Academic Press, NY, 1960, Chap. X.

10. J. Crank, "The Mathematics of Diffusion", Clarendon Press, Oxford, 1975

11. H.S. Carslaw and J.C. Jaeger, "Conduction of Heat in Solids",

Clarendon Press, Oxford, 1976.

12. J. Crank and G.S. Park, "Diffusion in Polymers", Academic Press, NY,

1968.

13.

E.G. Davis and M.L. Rooney, "Transport of Sulphur Dioxide in

Polymers", Kolloid-Z. und Z. Polymere 249 . 1043-1050(1971).

14. F. Lyth Hudson, R.L. Grant and J.A. Hockey, "The Pick-Up of Sulphur

Dioxide by Paper", J. Appi. Chem. 14, 444-447(1964).

45
15. C.J. Edwards, F. Lyth Hudson, and J.A. Hockey, "Sorption of Sulphur

Dioxide by Paper", J. Appl. Chem. 1^, 146-148(1968).

16. J.B. Atherton, F. Lyth Hudson, and J.A. Hockey, "The Effect of

Temperature, Light, and Some Transitional Metal Ions on the Sorption of

Sulphur Dioxide by Paper", J. Appl. Chem. Biotechnol. 23, 407-414(1973).

17. D.J. Spedding, Sulphur Dioxide Uptake by Limestone". Atmos. Env. 3,

683(1969).

18. G. Odian and R.L. Kruse, "Diffusional Effects in Radiation- Induced

Graft Polymerization", J. Poly. Sci., Part C 22, 691-712(1969).

19. P. Concus and D.R. Olander, "Transient Diffusion in Composite Slab",

Int. J. of Heat and Mass Transfer il, 10(1968).

20. G. Horvay, R. Mani, M.A. Veluswami and G.E. Zinmeister, "Transient

Heat Conduction in a laminated Slab", J. of Heat Transfer 95, 309-

316(1973)

21. J.C. Fisher, "Calculation of Diffusion Penetration Curves for Surface

and Grain Boundary Diffusion", J. Appl. Phys. 22, 74-77(1951).

22. R.T.P. Whipple, "Concentration Contours in Grain Boundary Diffusion",

Phil. Mag. U5, 1225-1236(1954).

23. C. Barnes, "Diffusion Through a Membrane", Physics 5,

4-8(1934)

24. H.W. March and W. Weaver, "The Diffusion Problem for a Solid in

Contact With a Stirred Liquid", Phys. Rev. 31 . 1072-1082(1928)

25.

L.H. Spinner, "Brightness Reversion", TAPPI 45(6) . 495-513(1962)

26. Dr. Charleton Bard, private communication.

27. L. Santucci and M.G. Zappala-Plossi , "Aging of Paper in a Closed

Tube", Problems of Conservation, Part II, p. 501-512, Ed. Compositor!,

Bologna, 1973 (In Italian).

28. C. Shahani, Abbey Newsletter, April, 1986, p.20.

29. D.W. Brown, R.E. Lowry and L.E. Smith, "Prediction of the Long Term

Stability of Polyester Based Recording Media", NBSIR 84-2988, National

Bureau of Standards, Gaithersburg, MD 1984.

30. ANSI Standard PH 1.43-1985, "Processed Safety Film- -Storage"

American National Standards Institute, NY.

46
31.

ANSI Standard PH 1.48-1982, "Black and White Photographic Prints -- Practice for Storage", American National Standards Institute, NY.

32. C. Shahani and W.K. Wilson, "Preservation of Libraries and Archives",

Am. Scientist 75 240-251(1987).

33. W.K. Wilson and E.J. Parks, "An Analysis of the Aging of Paper",

Restaurator 37-61(1979).

34. W.K. Wilson and S. Lee-Bechtold, "Guidelines for Environmental

Conditions for Storage of Paper-Based Records in Archives and Libraries",

to be published.

35. See ASTM Standards D3290-76; D3208-76; D3301-74; D3458-85, Book of

Standards, ASTM, Philadelphia, PA.

36. ANSI Standard Z 39.48-1984, Permanence of Paper for Printed Lbrary

Materials, American National Standards Institute, NY.

37. P. Luner, "Paper Permanence", TAPPI 52(5) . 796-805(1969).

38. A.E. Kimberley and B.W. Scribner, "Summary Report of Bureau of

Standards Research on Preservation of Records", National Bureau of

Standards Miscellaneous Publication M154, Washington, DC, 1937.

39. W.H. Langwell, "How Does Air Pollution Affect Paper?", Proc. Roy.

Inst, of Great Britain 210-214(1958).

40. F. Lyth-Hudson, "Acidity of 17th and 18th Century Books", Paper

Technology 8, 189-190, (1967).

41. N:S. Baer and S.M. Berman, "An Evaluation of the Statistical

Significance of Hudson's Data for 17th and 18th Century Books in Two

Libraries", Restaurator 7, 119-124(1986).

42. L.F. McBumey, Chap. 3 in "Cellulose", Vol.l, E. Ott and H.M. Spurlin,

Eds., Interscience, NY, 1954.

43. H.H.G. Jellinek and S. Igaroshi, "Determination of Diffusion

Coefficients for Nitrogen Dioxide in Polystyrene by <3hain Scission and

Sorption-Desorption", J. Phys. Chem. 74, 1409-1417(1970).

44. H.H.G. Jellinek, R. Yakota and Y. Itoh, "Reaction of Nitrogen Dioxide

with Nylon 66", Polymer J. 4, 601-606(1973).

45. W.T. Schreiber, A.L. Bullock and W.L. Ward, "Resistance of Partially

Acetylated Cotton Fabric to Nitrogen Dioxide and to Hydrogen Chloride",

Text. Res. J. 24, 819-822(1954).

46. H. Bogarty, R.S. Campbell and W.D. Appel, "The Oxidation of Cellulose

by Ozone in Small Concentrations", Text. Res. J. 22 , 81-83(1952).

47
47.

D.D. Roberson, "The Evaluation of Paper Permanence and Durability",

TAPPI liiili, 63-69(1976).

48. G, A. Richter and F.L. Weils, "Influence of Moisture in Accelerated

Aging of Cellulose", TAPPI 39(8) . 603-608(1956).

49. W.K. Wilson and E.J. Parks, "Comparison of Accelerated Aging of Book

Papers in 1937 with 36 Years of Natural Aging", Restaurator 4, 1-

55(1980).

50. W.K. Wilson, J.L. Harvey, J. Mandel and T. Worksman, "Acclerated

Aging of Record Papers Compared with Normal Aging", TAPPI 38(9) . 543-

548(1955)

51. H.P. Dixson, Jr. and J.C. Nelson, "An Accelerated Study of Several

Writing Papers", TAPPI, 45(10) . 753-760(1962).

52. W.J. Barrow, "An Accelerated Study of Several Papers; Re-evaluation

of Data", TAPPI 47(2) . 105-107(1964).

53. B.L. Browning and W.A. Wink, "Studies on the Permanence and

Durability of Paper. I. Prediction of Paper Permanence", TAPPI 51(4) . 156-163(1968)

54. G.G. Gray, "An Acclerated-Aging Study Comparing Rates vs. TAPPI

Standard 453", TAPPI 52(2) . 325-334(1969).

55. E.L. Graminski, E.J. Parks and E.E. Toth, "The Effects of Temperature

and Moisture on the Accelerated Aging of Paper" , in "Durability of

Macromoiecular Materials", R.K. Eby. Ed., American Chemical Society,

Washington, DC, 1979.

56. ASTM Standard D776-65 (Reapproved 1971), "Relative Stability of Paper

(Effect of Heat on Folding Endurance)," Book of Standards, ASTM,

Philadelphia, PA, 1987.

57. Standard T 453, "Effect of Heating on Folding Endurance (Relative

Stability of Paper)", TAPPI, Atlanta, GA.

58. B.L. Browning, Library Quarterly 40(1) . 18(1970).

59. R.D. Cardwell, "Aging of Paper", Doctoral Thesis, N.Y. State College

of Forestry, Syracuse, NY, 1973.

60. A.E. Kimberly, "The Deteriorative Effect of Sulphur Dioxide Upon

Paper in an Atmosphere of Constant Humidity and Temperature", Bureau of

Standards J. of Res. 159-171(1931).

61. W.H. Langwell, Proc. Tech Sec. Brit. Pap. Makrs . Ass. 37(3) . 495(1956). (Not seen.)

48
62. H.H.G. Jellinek and A.K. Chaudhuri, "Inhibited Degradation of Nylon

66 in Presence of Nitrogen Dioxide, Ozone, Air and Near-Ultraviolet

Radiation," J. Poly. Sci. Part A-1 10, 1773-1788(1972).

63. J.W. Mead, K.E. Mead, I. Auerbach and R.H. Erickson, "Accelerated

Aging of Nylon 66 and Kevlar 29 in Elevated Temperature, Elevated

Humidity, Smog, and Ozone," Ind Eng. Chem. Prod. Res. Dev. 21 , 158-

163(1982).

64. M. Igarashi and K.L. DeVries, "An E.S.R. Investigation of

Environmental Effects on Polymeric Materials I. Nylon," Polymer 24, 769-

782(1983)

65. M. Igarashi and K.L. DeVries, "An E.S.R. Investigation of

Environmental Effects on Polymeric Materials II. Polyethylene," Polymer

24, 1035-1041(1983).

66. R.M. Felder, R.D. Spencer and J.K. Ferrel, "Permaeation of Sulfur

Dioxide Through Polymers", J. Chem and Eng. Data 20, 235-242(1975).

67. D.W. Brubaker and K Kammermeyer , "Separation of Gases by Plastic

Membranes", Ind. Eng. Chem. 733(1954).

68. M. Benarie and Bui - the - Chuong , "On the Utilization of Various Plastic

Materials for Collection and Storage on Polluted Atmospheres", Atmos.

Env. 3, 474-477(1969). (In French.)

69. J. Honousek and L. Henryk, Chem. Listy 376(1962). (Not seen.)

Data from this source are of doubtful validity since time units were not

reported. See Ref. 62.

70. S. Jordan, Staub- Re inhalt Luft 32, 36(1973). (Not seen.)

71. V.L. Simril and A. Hershberger , "Permeability of Polymeric Films to

Gases", Modem Plastics 27, 95-102(July, 1950).

72. P. Y. Hsieh, "Diffusivity and Solubility of Gases", J. Appl. Poly.

Sci. 7, 1743(1963).

73. R.L. Feller, S.B. Lee and M. Curran, "Three Fundamental Aspects of

Cellulose Deterioration," Art and Archeo. Tech. Abstr. 22 ( 1 ) . 277-

357(1985).

49
TABLE 1

Empty Box

Full Box

Area

Diffusion

Dimensions of Prototypical Container

Volume, cm^ Area, cm^

11960 3070

2700 1420

Thickness of Wail 0.18 cm

Gap

7.62 cm

Length 3.28 cm

50
TABLE 2

Relaxation Times for Diffusion Into a Box With Unreactive Contents

Values are in seconds

D are in cm^/sec

D-10"® D-10'® Gaps

D-0.2

Empty Box 2.34x10® 2.34x10^ 2.50x10^

Full Box 1.14x10® 1.14x10^ 5.63x10®

51
TABLE 3

Values of 1+cj^r^ for Box Filled With Inert Contents

Difusion Through Walls Diffusion

Through Gaps

D=10"® D=1Q-9 D=0.2

4 1.02

Empty Box 202 2.01x10

Full Box 48.7 4.77x103 1.00

52
TABLE 4

Parameters for Box Filled With Reactive Documents

Unoccupied Volume,

cm^

Diffusion Through

Walls

7330

Diffusion Through

Gaps

7330

Volume of

cm^

Contents

4630 4630

Area, cm^ 3070 VO CM

Diffusion Length, cm 0.18 3.18

Diffusion

cm2/sec

Constant

10-

0.2

S 30 30

k, sec"^ 2.9x10'®; 830x10'® 2.9x10'®; 830x10'®

r , sec 2.85x10^ 1x10^

Tz , sec 3.63x10^; 1.26x10^ 3.63x107; 1.26x10^

’•1A2 0.79; 225 2.8x10'^ ; 0.08

53
TABLE 5

Concentration Ratios for Zero Flow Into Container

With Reactive Walls

kxl08 DxlO® C1 /C2 sec" ^ cm^/sec

11.6 1 0.84

2.9 1 0.96

11.6 0.1 0.28

2.9 0.1 0.663

115 1 0.28

29 1 0.663

115 0.1 0.0045

29 0.1 0.09

830 1 0.011

210 1 0.15

830 0.1 1.5x10"

210 0.1 5x10"*

54
TABLE 6

Concentration Ratios in Container With Reactive Walls

Half Filled With Reactive Contents

DxlO® k,xl0® k^xlO® C 1 /C2 cm^/sec sec" ^ sec" ^

0.1 2.9 2.9 0.094

0.1 2.9 830 ixia^

0.1 830 2.9 3.8x10"^

0.1 830 830 1x10"

1 2.9 2.9 0.54

1 2.9 830 9. 1x10"

1 830 2.9 4. 4x10"

1 830 830 2.4x10"'*

55
TABLE 7

Diffusion Into Book After One Day

Distance from Edge

of Book, cm

C1 /C2 Between Sheets

C1/C2

Center of Sheet

1 0.96 0.87

2 0.92 0.83

3 0.88 0.80

4 0.84 0.76

5 0.80 0.73

10 0.65 0.59

56
TABLE 8

Calculation of Reaction Rate Constant

From Data of Hudson

C,

x1Q5

m

sec" ^xl0^°

k

sec" ^xlO®

kCj/m

5 0.058 11.6 1,00

10 0.058 5.7 0,98

20 0.058 2.9 1.00

5 0.58 115 0,99

10 0.58 58 1,00

20 0.58 29 oo

5 4.1 830 1,01

10 4,1 410 1.01

20 4.1 209 1.02

57
TABLE 9

Transport Coefficients for SO2 In Various Materials

Material T,C Pxioioa DxlO®** S® Reference

Polyethylene 6.5- 9. 0-7.0 67

(Visqueen) 42

25 2.09* 112 0.0191 13

25 6.2^ 85.4

25 84.0 180 0.47 70

(Polyane) 22 43.4 3.0 1.45 68

(NSR-CSSR) 25 21.8-31.6** 69

Polypropylene

(Maurylene) 22 6.18 0.35 1.71 68

Po lycarbonate^ 25 17.5 0.63 2.96 13

Polyamide

(Nylon 11) 25 1.18^ 0.32^ 1.23^ 13

(Rilsan) 22 21.1 1.0 1.84 68

Po lye thylene

terephthlate

(Mylar) 22 5.27 0.16 3.29 68

Cellulose Films 22 52.7 2.7 1.98 68

Regenerated

Cellulose, dry 24.5 0.00172 71

100% Rh 24.5 37.9 69

Paper 25 1.31-6.74 69

Nitrocellulose 25 176 0.79 0.22 72

a) cm^ (STP) . cm/sec . cm^ . cmHg

b) cm^/sec

c) cm^ (STP)/cm^ . cmHg

d) See note on Ref. 69

e) SO2 partial pressure >25cm Hg.

f) For partial pressure of SO2 approaching zero.

58
FIGURE CAPTIONS

1. Drawing of the box used as the prototypical container.

2. One dimensional representation of diffusion into a container.

3 . Ratio of the interior and exterior concentrations as a function of time for the empty box or a box filled with

inert contents. F=Fuil; E=Empty. The numbers alongside the

curves are the values of the diffusion constant.

4. Assiimed exterior variation of pollutant concentration.

5. Assumed pressure or temperature variation. The variation

need not be linear between low and high values.

6. Ratio of the interior and exterior concentrations as a function of time for pressure and temperature cycling.

7. Ratio of the interior and exterior concentrations as a function of time for the box holding reactive documents. The

numbers beside the curves are the reaction rate constant and

the diffusion constant for the wail material.

8. Same as Fig. 7 but diffusion is through gaps.

9. Concentration of reacted pollutant in box contents as a function of time for diffusion through unreactive walls for

two values of the reaction rate constant. The straight lines

are in the absence of a container.

10. Same as Fig. 9, but diffusion is through gaps.

59
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25

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rttrApbchluc#

A Ai «3««ino*> irf><< nj snmji/lio^ b^J9s*i Ic joiyjn:>e»b0bO

10^ «iiBv AviS jA#"!^ dj|vo7d3 rrol«i^51b 3oi asU 5o fiol3a<»i4

23PiA<TJli O’fi ^ bai/Ia' cnr? .7A^iA3noo A ?o t^ABdA •«!? nt aia

CaUoXobb P:bn* 22 53.7 1> i- ^ « «« ^

R#|AnAcBt«d d^wTfi3 «; t?oi EiAllb •»!« *vi

CaIImIoba, «<4ry24.3 0 00172 r: 100% yi)

PApBT

Nictoc«U

24 5 %7.4

25 rn-4 ;

!

i /'t

m) «a* (4T?) e»/«#A .oiir* .ftaiff

V; ctt^/»0c

C) 5TP; /crs^ cmHj5

d) Sab fiot;A »o Eof.^v

a) S*^ b^tikl pr«AA\3r« >25^ H{,

. X') ?or y4£p}^l pr«*jfAur# cf 'SOj «p>.roA«h5i^ »awi.

•iS»

^!Sj
Fig. la

Side Elevation

(a)
Fig. 1b

Front Elevation

(b)
Impermeable

Walls

Rg. 2
I

Fig. 3

^0 / ^0

Time,
I

Rg.4

o

E

H

uoi)ej)uaouoo
Fig. 5

Pressure or Temperature
Fig. 6
Fig. 7

CM

T-OO ooooooo

o

O)

o

00

o

O

COO

IDo

o

CO

o

CMo

z 01 ^0

0)

Time,
Fig. 8

T-OO ooooooo

o>o

GOo

O

COO

lO

O

o

COO

CMo

(li

^0 /

'0

Time,
Fig. 9

Time,
Fig. 10

20/J0

Time,

APPENDICES

i • * *

•»r. !

r' 1

A » *

I n

Appendix A-1

In problems involving diffusion, and particularly when reactions are

involved, the questions of units and dimensions arise, and can often cause

confusion. In this Appendix, the conventions adopted in this report are given.

In addition, a material balance problem that arises when diffusion accompanied

by reaction occurs will be stated and solved. It is hoped that this will

alleviate, if not completely remove, questions that may arise in the treatments

of models to follow.

A. Definitions and Conventions

1. D is the diffusion constant. It has units cm^/sec.

2. C is concentration. It has dimensions amount/volume . Because we will need to be concerned with concentration of gases or vapors, we will always express "amount" as cm^ (STP) . Thus, for the gas phase

the concentration units will be cm^/cm^ , which is the same as mole

fraction in the ideal gas approximation, which is always used.'

Note that this is not a useful definition for gases unless the

total pressure is specified. In all the cases of concern in this

report the total pressure is always one atmosphere so that the

definition is useful. Considering the data availability and

quality, small differences from standard conditions are ignorable.

For concentration in the solid phase we will use cm^ STP/cm^ , i.e.,

the amount of material expressed as cm^ at Standard Temperature and

Pressure per cm^

We shall often be concerned with concentration inside and

outside a container, and concentration in the solid phase (usually

the walls or contents of a container) . We shall always denote the

A-1
interior concentration by and the exterior by C2 , except in

special circumstances.

The concentration in the solid phase will always be denoted

by C, using subscripts to denote more specific details about the

phase

3. S denotes the solubility coefficient. It is defined as

4.

5.

S = 1-1

where and are concentrations in the solid and gas phase,

respectively. Hence, with our definition for concentration, S is

dimensionless. Again, this is only useful at a specified total

pressure, which is always one atmosphere in the report. The small

difference between STP and the actual conditions is ignored since

we know the values of these quantities so poorly,

k is a first order reaction rate constant. It has units sec"^.

V is the volume of a container accessible to a pollutant . Thus it

consists of the unoccupied volume plus the "solution volume" of the

contents. Thus, if is the unoccupied volume and V^. is the

physical volume of the contents, then

V = + SV, 1-2

Its units are cm^

6. A is the area of a container by which pollutant has access to V.

Its units are cm^

7. i is the thickness of the wails of a container. Its units are cm. With these conventions and definitions, the flux of pollutant into a box

(see subsequent appendices) is in cm^/cm^ sec.

A-2
B. A Mass Balance Problem

We shall have occasion to be concerned with a container containing

reactive contents and into which there is a flux of pollutant. The pollutant

is soluble in the contents, but the rate of solution is rapid, so the reaction

is not diffusion limited. The contents react with the pollutant by a first

order reaction. We do a mass balance.

First, consider the contents. There will be some pollutant in solutions,

and some reacted pollutant. Let the total amount in the contents be A;. . Then

A, = As + A^ (1-3)

where Ag is the amount of pollutant in solution and A^ the amount reacted (i.e.

"fixed" or converted.) Then

dA„

dt _ ^dt dt

Now, if is the volume of contents and Cg and Cj. the respective

concentrations in amount/volume , this becomes

(1-4)

^ = V

^ + V

^

(1-5) dt « dt « dt ^ ^

Now consider the fluid phase in the container. By similar reasoning we have

dAf. _ y

^

dt ^ dt ( 1

- 6 ) If there is a total flux F of pollutant into the container, then clearly

F = ^

dt

^

dt

^ dt = dt = dt

(1-7)

By definition, and the assumption that solution is rapid, Cg = SC^

hence

( 1 F = V,

^ + V,S^ + V, ^ - 8 ) ^ dt ® dt = dt

or since V = +7^.3,

A-3
( 1 F = V

^ + Vg^ - 9 ) dt ® dt

This an equation we shall have occasion to use.

We can, however, go further. For a first order reaction, we have

or

( 1

- 10 )

Vc

^ = V.kSCj (1,-11)

which we shall also have occasion to use in calculating the extent of reaction

in the contents. Note that with our previous definitions, .

A-4
Appendix A

Diffusion Into an Empty Container or a Container Holding Inert Documents -Exact

Solution.

Referring to Fig. 2 of the text, we have this boundary value problem:

ac a^c

at

^ (2-1)

C(X,0) = C^(X ) (2-2)

C(0,t) = sCi(t): Ci(0) = Ci° (2-3)

C(i,t) = SC2 (2-4)

dC, AD ac at V ax x=o

(2-5)

where S is the solubility coefficient. It is assumed that the interior

concentration, Cj^

is not dependent on position (i.e. , it is "stirred"). The

solution is based upon those given by Barnes (23) and March and Weaver (24)

Let C = C’ + C" (2-6)

/ Where C' satisfies (2-2) and is zero at X=0 and X=i.

Then

C' = X

1 C„exp(-Oj,t) Sin ^

(2-7)

Dn^?r^

“n - ( 2

- 8 )

Cn = 7 J Ce(x) Sin —

o (2-9)

Following Carslaw and Jaeger, ((1) p. 102) C" is obtained from

•t r =

I [

C,(t)f^F,(t-r)+C,fjF3(t-r) ]dr ( 2 - 10 )

where

- . X 2 nTTX r 4.1 ( 2 - 11 )

1
(2-12)

_ X . 2 V/ \nlo- r F2 = I

+ - exp [-a,t

Eq. 10 can be transformed to

j- = Ci°Fi(x,t) + C2F2(x,t)

.t I

[ci'(r)Fi(X,t-r) + C2 ' (r )F2 (x, t-r

) j dr (2-13)

where the prime on and C2 denote differentiation. Now sum Eq. 7 and Eq

differentiate with respect to x,and take the limit as x-^0. Then use Eq. 2- obtain

£s - Cl - 2lD, exp.[-<»ntl

with

2 I I

(t) exp. [-a^(t-r) |dt

nw

D„ = - (-)“C2 - f- C

(2-14)

(2-15)

Eq, 2-14 is an integro-differentiai equation for . It may be solved as follows. Assume Cj^ ' may be written as a series of exponentials:

Cl ' = Ai X exp. (-^t t)

i

We know that as t-»«, C-+C2 , and hence

Ci(t) = C2 - X 7^ exp (-lit)

Si

Substituting Eq. 2-16 into Eq. 2-14 leads to the following:

iV

ADS li

and

- ^ + 2

n

= 0

(2-16)

(2-17)

(2-18)

D„ = Ci(o) - (-)“C2 - ~ C„ = X (2-19)

“n

-

Eqs. 2-18 and 2-19 form an infinite set of non linear equations for the 1^

Ai . Eq. 2-18, however may be transformed as follows. Define

Zi^ = (2-20)

13.

5 to

and

2
then it may be shown that Eq. (2-18) for the results in the following

V Cot Z, ^ Q AiS ( 2 - 21 ) The scheme for the solution is now clear. It goes as follows.

1) A, D, V, i and S are ass\amed known, as are the exterior concentration C2 the interior concentration , and the concentration profile C(x) in the

container walls when the container is closed.

2) From C(x) calculate by Eq. 2-9.

3) From these and C2 and , calculate by Eq. 2-19.

4) With the values of D, V, A and S calculate the roots of Eq. 2-19, and

hence the f ^

5) With these, calculate the A^^ from Eqs. 2-19. One trial has shown that

three of these are sufficient to get a good approximate solution.

6) Having the and Eq. 2-17 gives the time dependence of . This is clearly a rather tedious procedure, but it is amenable to

programming on a computer.

3
l'

- a j) »itj **i <8i-j) .ps

tf, t.?sn«to>raM*(i <31

2iwiJ mrodt •<! \Mm 2li“

a. :3) ^ .X 2^ V

au

x^io »/ «oJ2jiio« •ft? xol t2L»i{a« « C.*f,<*,6)' * ijFjiiii.E 3

'- ,0 rToj 7 ft$4a43Q<>3 »<lJ •!» ** ip»«>fDJ 6*«i/*»* nfc 8 bn* I ,V ,0 .A

n {s»3^lUill<i^^ft6i3^iSBiWA& • " »(U I^EP aaUntamjaai, -|oli*3«t<*fl3

*0 I * b»»oid «i #Kl nXlAw x#ni»liTOd

^ Kl«ia th* ptlfUl OtI C| •S^d C, 0\Ci«r<inct44:lim. «!*• Cl- ? T<j. T*.

diCf«ceaCl4^A to . . Pfki f

Obtain Ja ,*{0 bn« jP brt» •••rt? voil <i

:C^r^.ti^c ;j>StiA i&ioT*-*;3'

bn* a ,l 3 ,a lo «*ui*v .jo

^

- ajt Jc,' re) <i«p. • • Me

3*d3 owof^ »B.-f*i»jT* «lO .«J'S .»pl aoxi ^ *>to •ibii/?!** .•••r(3 *riV/.i

»2* ••dJ \o ••irt:^ - C;’' - iO*v.j ' j ^

, ^0 Uo 5 ••vlxi Tl-X- .p3 , i*<?# |A •/??

94 2-14 ts ma ^ ’ a ; ^

for C, -^i 1 ^

CkJ •Iduitmo •! si 7u*i jq ^wdtwR • 4

Coilovt. • mmf b# ^r;.Ct« •’ *• MrUi «l «>t*«aicmAla _

.x*2t>t7»03 A no gnlesAXSOT^^

'•V r Xp. I c)

i

U)^

kr^ ebAC aa OC^, Ant tv«Y'A:A C|^t> • C, * £ IjAAp (-itt.'

Sybacicvciilg tq. 2-1$ Into :!-14 i4«. !» ro dtA fAUqwlit^;

1

' (2-y>

tn4

r -i-' ^ ^ ^ • Iv «•. * U

:-iP

’ • j iq*. 2*111 AOfJ 2 '19 tom An tnflnlt# «et of noa llmaar AquAClonji fAt and

1 4 2-lR, hA%»*v«f ttAV b« CrArmfoEBkAd

,# 2/ - ^l^/» ,.:l

r- lVtoA** : OatlBA

f2*2&i

O

ii

iLMt

*.t''
Appendix A

Diffusion Into an Empty container or a Container Holding Inert Documents

Approximate Solution, Constant Exterior Concentration

The situation is the same as in A-1, but we make the approximation that

the concentration in the membrane varies linearly with position. The flxix of

pollutant into the container is then

F = D

where C(i) and C(o) are the concentrations in the membrane at x = i and x = o respectively. These are related to the concentration in the gas phase by

C(i) = SC2 (3-2)

C(o) = SCi (3-3)

where S is the solubility coefficient, and is assumed to be independent of

concentration. For dif;fusion through gaps, clearly S=1 . Then, the rate of

change of concentration in the interior of the container is

=-^ (C, - C,) (3-4) at Vi

Since for this case C2 is a constant, this equation has the solution

Cl = C2

- (C2

- Cl'*) exp (-t/r) (3-5)

or

C 1 /C2 = 1 - (1 - C 1 VC2 ) exp (-t/r) (3-6)

where C^® is the initial concentration inside the container (i.e., when it is

closed or placed into an atmosphere of concentration C2 ) and r is given by

r Vi

ADS

(3-7)

Hence r serves the function of a relaxation time. It depends upon the design

of the container via V, A and i, and upon the material of construction via D

and S.
Appendix A

Diffusion Into an Empty Container or a Container Holding Inert Docioments - Approximate Solution, Varying Exterior Concentration.

This model is the same as that in A- 2 except that the exterior

concentration varies with time. Referring to Fig. 4, we take it to be

where w is the angular frequency of the variation, i.e., 2?r/period. The

differential equation for the rate of change of interior concentration then

becomes

where the terms have the same meaning as before (See A-1, A-2, Fig. 2). This

equation is solved by standard methods to give

where again r = Vi/ADS, tan5 = -wr

and a is a constant to be determined by the

initial condition. Thus, at t = o we obtain

The last term will be small if wr»l or wr«l . This is the situation for the

cases investigated. Moreover, even if this were not the case, it would only be

necessary to take the zero of time a little differently in order to ignore the

last term. Hence it is dropped, and with this approximation the final result

is

Cj = Cg + Cj sin C4)t (4-1)

(4-2)

Cj^ =E aexp (-t/r) + Cg +

C^Sin(cjt-h5)

1+w^r^ (4-3)

Ci° = a + Cg +

C^Sin5

1+w^

(4-4)

(4-5)
Appendix A

Flows Through Gaps by Pressure and Temperature Changes - The "Breathing" Modes.

Consider a container of volume V containing gas, which is assumed to be

ideal. The moles of gas in the container is given by

where P is the pressure, T the temperature and R the gas constant. Since V is

a constant, n will change as P and T change.

^= 52 . « ( 5 . 2 ) n P T

^ '

This equation shows that an increase in pressure and a decrease in temperature

both increase the amount of gas in the box. This can only come about by

drawing in gas from the exterior. This gas will carry pollutant with it, and

if the concentration of the exterior gas is different from the interior, the

interior concentration will be changed. Conversely, as the pressure decreases

or this temperature increases, gas will be exhausted, but this will not change

this concentration.

We now solve for the concentration changes. In what follows,

concentration will be expressed as mole fraction, X, which is the same as volume fraction, C. Inside the container, let the number of moles of pollutant

be nj^, and the Siam of all other species be nj^b • Then the mole fraction of

pollutant is

n =PV/RT ( 5 - 1 )

( 5 - 3 ) and ^ a ^Ib ( 5 - 4 )

1
From Eq. 5-3 we obtain

dX, =

n

X1 a dn

n

(5-5)

But dnj^g is just the number of moles of pollutant carried in by exterior gas.

Hence we have

dni. = X2,dn (5-6)

where X£a is the concentration of pollutant in the exterior. Hence we obtain

dXi. = (Xj. - X,.)

dn

n

(5-7)

Now assume that only the pressure has changed. Then, using Eq. 5-2 we obtain

dX

X,

1.8. P (5-8)

^2 a a Consider now that we are undergoing pressure cycles as shown in Fig. 5. We

integrate Eq. 5-8 from the start of the i'th increase to its end, which we call

i+1 . Then we obtain

-in X7 , -X, , , ^ , ^2 a *^la »i in

For the next cycle we obtain

-in

^2e "^la »1 + 1 = in

(5-9)

(5-10)

But the pressure change is the same for ail cycles. Hence by summing Eqs

5-9

and 5-10 we obtain

-in X7 ^ -Xi , , 4 ^2 a "Xi, ,

(5-11)

where and P^ are the pressures at the end and beginning of the pressure

rise. Clearly, if we start with the first and carried out N pressure cycles we obtain
-in = Nin 1^- (5-12)

This can be solved for to give

Xi..» = Xj. - (X^. - [1^]

N

(5-13)

Recalling that volume fraction is the same as mole fraction, we obtain

^ = 1 -( 1

- fe]

N

(5-14)

^2 ^2

For temperature cycles, the analysis proceeds in exactly the same manner, but

because of the minus sign in Eq. 5-2, the result is

Eqs. 5-14 and 5-15 are those discussed in the text.

(5-15)

3
I

1

tJ-O 4 a»» • n'

i » • I** • c*

•Vl| o:J K,,;X lo5 b®^io«.

But jute ch4k jumb€t 0r*t^«* uf luc«/it c#nri«4 vn by *aitrl&g. ji«

diirw,» C^*tUv»

nli^3b>«* *»»1^3»3i •Ion «• •••* •'<* noJ33»iJ a^iov 3«itt58*>Ii*!

"''"2 I I '’!

^4vtc* Xn« if di4 <ioRctTm:tfri»n '»g In rh» Mttrior. Etoct W obtiitelj

w)

•> •’ ' '

4r» (^i-2) P V _ ^ _

3iid Vii^i xl^*

^ .»fa* M,u»* rj«t »nl> th.

( j]

1) - I ^a.rS') jj. r

COfU»ldit7 ntv #x« uod«tt(.ixr, iia to#w ..p

illtt$rtt« Sq, 5*4 fto« Ch» 7h« C*Cih ‘rv.r»# i ‘.4 tn4a. cti. V

1-^i TH«t‘, w<« ©bttlw

f

Ifl

Tor ih< <:vcl« vt obctln

-#0 ^A.-.5lA.tlT-I, « fu (I

bvif, ch4jpttMur% <h^n$m ia %kl§ ttfx «U il«rc« by tut»£&4

«to4 ^'16 irt obe»ln

&

» .X':..^i ,. ‘>

tfhmt* Aful ?| c5ia

^

•Ml Wf.'uv* of cb# j*rftG 4

rlfAr Cl«Ail]rv HlVt fttrt «;ii) chA tifr And 4as*1«<i1 ouc H w>cl4» Mt

ahttito ‘i“

<

' f ,11)

I * 'i

A.
Appendix A

The Container with Reactive Contents - Exact Solution

This solution follows in exact parallel the solution in Appendix A-2.

The only difference is in Eq. 2-5 of that Appendix. Hence we have the

following boundary value problems

dC _ d^C

dt dx^

C(x,o) = Cg (x)

(6-1)

(6-2)

C(o.t) = SCi(t); C^(o) = Ci° (6-3)

C(i,t) = SC2 (6-4)

3C, _ AD ac V^kSC^

(6-5) at V ax x=0 V

The final eq\iation follows the material balance considerations given in A-1.

It simply states that the rate of change of concentration is the difference

between the flux of pollutant into the container and the rate at which it

reacts with the contents

Proceeding as in A-1, we obtain

Vi aCi V.kiC, ^ ADS = C2-Ci-2XD„exp(-a„t)

-2X

J

C'exp[-a„(t-r)] dr

This is an integro-differential equation for Cj^ . Again we let

( 6 - 6 )

dC,

dt

-t?i (6-7)

giving
Cl = Cl- - X (6-8) .-tei

where Ci* now is not C2 , but the steady state value of . Substituting Eqs

6-7 and 6-8 into Eq. 6-6 we obtain

Dn = Z (6-9)

and

LL . ^ [YcM + 1] ^ 2 y = 0

DAS Cl [da ( 6 - 10 )

where , as in A- 2 is

nTT D, = qo - (.)"C2 - f- C„ ( 6 - 11 ) Equations (6-9) and 6-10 are again infinite sets of non-linear equations for

the Ai and Ci • Proceeding as before, Eq. 6-10 maybe simplified. Again define = ?i-«VD (6-12)

A certain amount of manipulation now yields an equation for the and hence

the Ci : -

V V.ik 1 _ Cot Z, , .. iAS ' DA Zi

This equation can very likely be solved for the Z^ by numerical methods, but

this was not attempted. The scheme for the solution would proceed as in A-2.

2
Appendix A

The Container With Reactive Contents- Approximate Solution

As in A- 2, we assume that the concentration in the wails of the container

varies linearly with position. It is assumed that diffusion into the contents

is rapid so that their reaction with the pollutant is not controlled by the

rate of diffusion into them. This will be approximated more closely if the

contents are not tightly packed. Then, equating the rate of change of

concentration inside the container to the flux into it minus the rate of

reaction with the contents, as described in A-1, we obtain

^ ^

(C(i) . c(o)) - dt Vi ^ ^ ^ V

and from the definition of S in A-1,

~ \7 0 ^^2 " /

(7-1)

(7-2) at Vi "''2 V

where it has been assumed that the solubility coefficient for the contents is

the same as for the wails. This is obviously easily rectified.

Eq. 7-2 is a differential equation for Cj^ . It is solved by standard

means to yield, for C2 a constant.

1 1+^1 /T2

where = Vi/ADS and T 2 = V/V^kS.

This equation is very similar to Eq. 3-6 of A- 3. Only the factor t^/t 2 and the factor in the argument of the exponential term make it different. An

important point is to notice that the relaxation time for this process is

smaller than either or . If we denote the relaxation time by rg , then it

1
follows directly that

(7-4)

which is smaller than either or T 2 . Further details of the behavior are

given in the text.

The increase of concentration of reacted pollutant in the contents is

easily calculated from these results. From the first order reaction we have,

following Appendix 1,

= k C, (7-5)

where is the concentration of reacted pollutant in the contents and Cc is

the concentration of unreacted pollutant.

But since Cc = SCj^ , we obtain

where Cj.° is the concentration of reacted pollutant at the initial time. An

important point is that after a very long time and the exponential term has

become negligible, reaction continues. This is discussed more fully in the

main text.

(7-6)

2
Appendix A

Container with Reactive Contents - Approximate Solution, Time Varying Exterior

Concentration

This model is treated in exact parallel with A- 7, except that the

exterior concentration now varies with time. Assuming the time variation to be

as in A-4, we obtain for the basic differential equation for the concentration

inside the container.

dC,

at

ADS

(Cg+Cf Sinwt-Cj^ )

- V.kS

v-c—f 1/ V

where ail the symbols have been previously defined,

is easily solved by standard methods to yield

( 8 - 1 )

This differential equation

Sin(g?t+a)

1+w^ (8-2)

where a is a constant to be determined by the initial conditions, and

TiT 2 /t^+T2 . Using the same approximations as in A-4, we obtain

= 1 - (1

^ -t/r. C^ 1 Sin(ojt+5)

> « ^cf(l+r,A,) (3-3)

The concentration of reacted pollutants in the contents easily can be

calculated from this equation, but was not done since it would add no new

insight.
m..

» ‘ V

-:

, i,*r

<.

. I H'A jfibir^qqA

7 d1 i«Jx3 ylYi*y, ,/iolJi/io^ aJi^HxcnqqA -

whleh ii ttuus •‘cij^f iVt # irctiAr ^ •’.•hAviot

fri3 Jiul^ 3q»*ijc» ,T*A rfalw l^iUjjiq nl l»«3*eT3

^ J^on mirfl

In t:*f- fpjct.

V mU3 #{tj ,*«W xl3tw ft»l3AV WOXJ i>ol3*13n«300» 'lOl'l^Ji

T!i^i ifwrtM of cr-r^fiopj^iiOfi r»*op«Hi peril i^^nt lu tttp •-.or.un-cjr i«

nqi3Att^«k^ot> wib ^cl oitad •fb ’Jol iU*3«io o«h ,a-a ni •0»liy i!AT«UiAe4i4 fiM Tr*^ rhm i$tst i»r«ttr e**«c^lr-n ¥» H^'*.

fdUWlin^ Appendix t,'

3onlA3a9Q fft^

tt'd U ^ SdA >0^

»>«Mr|0Jfiyp A si *n>ti <riJ? (ji^^

«***^

th. aone^ttCWfcUii of yau^Ji r< . ^ ^

But: «ur

(S

^ SC| • c A I?

" h*-j^)ntZ .3 . .Atitot> (( «i o mt9t V3C t aIS ^ T •

*

*^U •* S^J^'l'jytAjAcV

vh4r« c,* AOfiftcnarAtlofi At ro«< a * f^Ui^nxcnt «: :Sii initlqlyij 4. .ct

Import u^nffpllnt u th4t^4t|iip^ thi ijtpjBA-jcilr t£ti '|i

t>«coM &3H«S^o» ^ito ai-4ii*4ii’ilAq'«BMCi**srA0?n4lT*1^t%iO» •< Mfn e«||,„ J,tu^ ,l *-j„i, WI0I> ;an ,t»0l3»i/?» *Jrfs •<>« b*3»l"3J»i

I . J‘ ' t

/V**

•SII \r.
Appendix A

Empty Container With Reactive Wails: Exact Solution

In this model we consider an empty container, but the walls are of

material that can react with the pollutant by a first order reaction as the

pollutant diffuses through them. All problems of combined diffusion and

reaction are difficult, and the exact solution is sketched out because it

appears not to exist in the literature and because it is an important model.

For diffusion with first order reaction, the basic diffusion equation is

i£

at

(9-1)

The boundary conditions are the same as in A-2, again assuming that does not

vary with position thus

C(X,0) = Co (X) (9-2)

C(0,t) = SCi(t), Ci(0) = (9-3)

C(i^t) = SC2,(t) (9-4)

ac, AD

at V

dC

dx x=o

(9-5)

Now define C, (X,t) by the equation

C = C, e-^^ (9-6)

then Eqs. 9-1 to 9-5 become

ac, ^ at

^

a^c.

(9-7)

C, (X,0) = c^ (X) (9-8)

C,(o,t) = SCi(t)e^^ (9-9)

c,(i,t) = SCje'''^ (9-10)

dC, AD

at V ® ox x=o

(9-11)

1
Eqs. 9-7 to 9-11 now form a boundary value problem with time dependent boundary

conditions, and we use the same methods in solving it. A rather tedious

algebraic manipulation leads to the following equation

Vi dC, ^

ADS at 2 Ci(t) - 2 X Dne-'*^

1

+ 2

- 2 (r)+kq(r)

•]

exp -/c(t-r) dr (9-12)

where

%

Cn

D 2^2 + k

- (-)“C2 - f- C,

i

C„(x) Sin di

(9-13)

(9-14)

(9-15)

And all the other quantities have the same meaning as previously.

Eq. 9-12 is an integro- differential equation for , and is the analogue

of Eq. 2-14. Indeed, it will be seen that the former reduces to the latter as

«-*>o, as it must. However, it is not clear that the methods used in A- 2 will

solve Eq. 9-12. Machine methods might be used, but the matter was not pursued

as being too detailed for the purposes of this study.

2
Appendix A- 10

Container With Reactive Walls: Steady State Solution

A. Introduction

Because reaction as well as diffusion is taking place in the walls, it

was felt that it would not be realistic to assume a linear concentration

gradient in the walls. Then, since the exact solution given in A-9 is far too

complex to use, the only approximate solution that can be obtained is at steady

state. This occurs a long time after the container has been sealed, after all

the transients solved for in previous Appendices have died out. This is

obviously a limited approach, but fortunately gives considerable insight. In

this model, the exterior concentration is assumed to be constant. First we

consider an empty container, then one filled with reactive contents.

B . Empty Container

At steady state, the boundary value problem in A-9 reduces to the

following

D 0 -kC = 0 (10-1)

C(o) = SCi (10-2)

C(i) = SC2 (10-3)

Eq. 10-1 is easily solved in terms of hyperbolic sines and cosines. The

solution that satisfies Eqs. 10-2 and 10-3 is

C = C^S Cosh rX + SC^-Sq Cosh ri

(10-4) ^ Sinh ri ^ ^ where r = (k/D)^^^

1
Note that this gives only the concentration profile in the walls of the

container. That in itself is of little use. However, from it we can calculate

the flux into the container from Pick's first law of diffusion:

F = D ~3x x=o

Carrying this out gives

„ \ 1 / 9 SC^ “Ci S Cosh r.2)

^ knh ri

^

(10-5)

( 10 - 6 )

If the box is empty, i.e., with nothing in it to consume this flux, the

fltix must be zero. This gives the interesting result for the ratio of Cj^/C2 to

be zero

An explanation of this result is given in the text.

C. Container with Reactive Contents

As already mentioned above, if the container is not empty, the flux of

pollutant into the container must be consumed by the contents at just such a rate as to keep the concentration constant, as it must be at steady state.

However, the rate of reaction depends upon C^ so we must first find the value

of C^ at which the rate of reaction is just equal to the total flux.

To proceed, we must be careful of our constants. The reactivity of the

contents need not be the same as the reactivity of the walls. Hence in what

follows we let Iq, be the reaction rate constant for the walls and k^ that for

the constants. Now, as discussed in A-1, the total rate of reaction of

pollutant with the contents is given by

2
= V,k,c, = V,k,sq ( 10 - 8 ) dC,

dt

Equating this to the total flux we obtain

V.k^SCj = A (Dk„)i'2 (SC, -SCi Cosh r„i)

Sinh r^i

where = (lq,/D)^^^

( 10 - 9 )

Solving this for Cj^ gives

Cl Vc K

A y Dls,

C,

Sinh r^i + Cosh r^i

( 10 - 10 )

Now having the steady state value of , we can calculate the rate of

increase of reacted pollutant in the contents simply by multiplying this by

kgS. Without a container, the rate would be simply kSC2

.

3
ciwit profile U\ ch* of

ThAK % t%

< 8-00

flu» itlt0

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If thm t m 1* 0wpfy. . trUllla^f in ic ;qd oottmiA^ tht» fJLuK,^

^ ^ —I ^ . TTTI^irS "

4 V. (Itof iiwjjc w TtiU i^lirna r;.e t t « fA4^!A^*fA\ii e ArWk

‘'~^r ^d 0^9.j orfa »3aU3 Uo n%o wv ,p lo owlav #3 a3» m/U jflivwf vo«

^' • ^ ci/tJ ifflxlqlaXt^ »^fT»3fio:> tsi Jn^yilog l»«3a^3

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w;iq«tg i»d bXt/OW OXAl orf3 . iwil*3/too A 3HfjrC»^ .8

4^ 4xpUr.Arlon of rJ4« taf^Xr la glvaa its ti « taxc

C Coot«i;i«r vifh f x ct^iNi OoiUjtna#

K >j atficioMi^ abvff th*' ^ottc tnar it 'h-« ^tuafoi

tnra th# COafi«lM«r t^« c r.f>tts«^ hy riaO n«|||UBMti a". jU«s jit

t*ta> M t» V*«|^ ^otKiAOCtAHori n^oJkr ^ if, gf apuit bo -%K- F''^*AdV : xC4iS'r!i

itovoi'or, cX)o mao osf foacctoo * c, ?o %« iiruot ftrat

of C;l Af Whl4h thu r«c« ot r«4i£r.lon l« Juoc C4 r:hih cofAi flux.

To proc»4^W.« Ott opgati ba 4i«r«liAl of ct

’- rv . cotiCATiCf ooii'1 r^oc b# uho (K»o tHo r«vKt|vlc;y of -ho a«llAs J'.oika *^yiiiJ£‘^

*• ^ CtflXo«#» v« let k,, ||« t( A roAatloTi rot* cofUiCAnr far ehe >oP.i aiv.^ k, .:.tt .ftr

r-ha v'^an>t4iAt9. flow, a« 4lAuu«se4 itt A l. th * : >^rol TMC» of nMtftlon aC)^

wlrh tbo iy:tit<»ntJi U fivon by . ,
Appendix A- 11

Sorption in a Sheet with Reaction

For this model, imagine a sheet of thickness 2i immersed in an atmosphere

containing pollutant. Pollutant diffuses into the sheet and reacts with it.

This is the model described in A- 9 and A- 10, but with Cj^ = ^2 . Because the

time -dependent solution is too complex to be useful, only the steady state

solution will be given. This problem has been solved by Odian & Kruse (18).

Note that at steady state, the concentration profile of unreacted pollution

does not change, but the concentration of reacted pollutant increases steadily.

Following A- 10, ass\ome the sheet thickness extends from -i to +i, so that

its thickness in now 2i. The boundary value problem now becomes

D 0 - kC = 0 (11-1)

C(i) = C(-i) = Cj (11-2)

where is the surface concentration, the solution to this is

. . ^

C, Cosh rx

^ Cosh ri

where r = (k/D)^^^

The average concentration of unreacted pollutant is

.i = - f 2i J C(x) dx

-i

(11-3)

(11-4)

which yields

r _ ^ tanh ri

^

i r (11-5)

Since the rate of increase of the concentration of reacted pollutants is k C,

the slope m of the curve of reacted pollutant concentration vs time is

1
m ( 11 - 6 ) C. k tanh ri

i r

This may be cast in the more convenient form for solution by iteration — — — = tanh 7k — (11-7)

C3 7d a 7d

2
ADDENDUM

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t

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. At

SA

M

Sf

u

AS •
fori* tor If it«rALi»Q ,
ADDENDUM

Temperature and Water Vapor Microenvironments

A.l Introduction

With good temperature and relative humidity control in the archive

stacks, these microenvironments are not expected to be greatly different from

the macroenvironment. However, for the sake of completeness, temperature and

water vapor microenvironments are discussed in this Addendum.

A. 2 The Temperature Microenvironment

The temperature microenvironment is important because the rate of

degradation reactions generally varies with temperature, specifically according

to the Arrhenius law. As the temperature of the stacks varies, so will the

temperature inside a container filled with documents, or in the interior of a book. As is readily apparent, however, the temperature in the interior will lag

that in the exterior, and, if the exterior temperature cycles with a given

excursion, the interior temperature will cycle with a smaller excursion, whose

magnitude, however, will depend on the position in the book or container. At

the very edge of the book or container, the temperature will be the same as the

exterior temperature. At the center of the book or container, the temperature

variation may be only a small fraction of the exterior variation, depending on

the period of the cycling, the size of the book or container, and the thermal

conductivity, or more precisely, the thermal diffusivity, which is the ratio

of the thermal conductivity to the product of specific heat and density. The

only question that arises is the magnitude of the effect.

To illustrate this, we have made calculations for three specific cases: an isolated book; a document box; and a row of books tightly packed on a bookshelf. In each case it is assumed that initially the temperature in each of

these three items is uniform. At a given time, the exterior temperature is

changed by a given number of degrees. We ask, "What is the temperature as a function of time and position inside the item in question?"

To solve this problem we need to know the values of thermal conductivity,

specific heat, and density for the material in the book, -document box, and

shelf of books. First, consider the book. Except for the cover, the book may be

considered to be a solid block of paper. Now, the American Institute of Physics

Handbook (1) gives the thermal conductivity of rice paper and blotting paper as 0.00011 and 0.00015 cal/cm^/K/sec respectively. The specific heat of most

cellulose- like polymers is approximately 0.3cal/gmK, and we have taken the

density to be unity. More accurate values are not necessary for our semiquantitative purposes. Hence we obtain the value of 0 . 0004cm^/sec for the

thermal diffusivity. We have also assumed that the book covers have the same diffusivity, which is reasonable for our purposes.

The situation for the document box is somewhat different. Here there is an air space. The thermal conductivity of air is quite low, being about half

AD-1
that of the paper given above. However, the thermal diffusivity is very high

because of the low specific heat and density. To solve the container problem

exactly becomes one of the Models Not Solved in Sec. 2.10. We have instead done

a simpler problem and assumed that the container is tightly packed with

documents , ignoring the air space

Each of these problems then becomes that of calculating the temperature

as a function of position and time in a rectangular parallelipiped which was

originally at a uniform temperature and is suddenly placed in an environment at a different temperature. This is a standard problem in Fourier series whose

solution is given in standard texts (3,4). This solution was used to calculate

the temperature -time -position curves in Figs. A-1 to A-3. Obviously, there is

an infinity of positions that could that be chosen, but only a few were, as discussed for each separate set of curves

Fig. A-1 is for an isolated book. Its dimensions are 5cmxl6 . 5cmx24 . 8cm.

The positions chosen area at the center of the book, and along the 5cm

dimension at the midpoint of the other dimensions. The results are given as (T-Tg )/(Tq -T, )

where T^ is the exterior temperature and Tq is the original

uniform temperature. Clearly, the curves can be scaled for any temperature

difference (Tg-T,

by simply multiplying the ordinate by this value. Curves are given for lOmin, . 40min, Ihr, and 4hrs. Also indicated by the dashed line is

the temperature distribution at zero time, i.e., the time at which the external

temperature was suddenly changed. After nine hours (not shown) the whole book

is essentially at the temperature of the exterior. As expected, the center of

the book is the slowest to change, and the surface regions change most rapidly.

This will become more apparent in subsequent figures.

Figure A- 2 is the analogue of Fig. A-1, but for the prototypical

container tightly packed with documents. This again is treated as rectangular

parallelipiped. The dimensions are 12cmx26cmx38cm, and again the temperatures

are along’ the short dimension along the center line of the container. Here

curves are given for 1,4, 9, 16 and 25 hrs. As compared with Fig. A-1, changes

are much slower in the interior of the container, due, of course, to the

greater thickness. Here, after one hour, approximately 60% of this region of

the container has changed in temperature by less than 10% of the temperature

change, while the remainder has changed by an average of about 50%.

Finally, in Fig. A-3 we show what happens when books are tightly packed

on a shelf. Here the shelf is 85cm long (the dimension of a bookshelf in the

Polymers Division Library) , and the lateral dimensions of the books were taken

to be 16 . 5cmx24 . 8cm. Temperatures were calculated along the 16.5cm dimension at

the mid-point of the book stack. It was to be expected that the temperature

changes in this case would the slowest of the three cases studied, and this is

borne out as shown in Fig. A-3. Here, after one hour, in this region of the

stack of books, a full 50% of the book has shown essentially no temperature

change, and about 75% has shown and average temperature change of less than one degree

It is clear from physical reasoning and could easily be shown by more

extensive calculations that the faces, edges and corners of books, stacks of

books, and document boxes follow temperature excursions more closely than the

AD-2
interiors of these items. The interior is "shieided" from changes occurring in

the exterior. It seems reasonably clear that, given regular changes is the

exterior, at steady state the center of the item will be at the average

temperature with small changes that mimic the exterior, while the surface

regions will follow the exterior changes, but less and less closely depending

on the depth.

What use is to be made of these data? Clearly, what we are interested in

is not the temperature per se

but the extent of reaction. We therefore now

consider how this information on temperature as a function of time and position

can be used to calculate the extent of reaction also as a function of time and

position. For the sake of illustration, assume we are interested in a property

such as specific absorption coefficient, A. Other properties could be used; all

that is required is that the rate law be known. Then, as shown by Browning and

Wink (5), A varies with time as follows:

dA/dt = k (Al)

The rate constant k is a function of temperature and follows the Arrhenius law,

which we may write as follows:

k = kg exp[ -AH/RT] (A2)

Now, the temperature is a function of position, x,y,z, and time, t, and

therefore so also will be the rate constant, as follows:

k = kg exp [ -AH/RT(x,y , z ; t) ] (A3)

Hence, at any point x,y,z we can write

dA(x,y,z; t)/dt = kg exp[ -AH/RT(x,y , z ; t)(A4)

Finally, for the change in the A at a point x,y,z after exposure to a temperature T for a time t, we obtain the following

t

A(x,y,z;t) - Ag - kg exp [ -AH/RT(x,y , z ; t] )dt

0

(A5)

where Ag is the specific absorption coefficient at zero time. What this

equation shows is that knowing the temperature as a function of time and

position, the change in A can be calculated as a function of time and position

by carrying out the integration, which would generally have to be done

numerically. If, for example, the temperature around a book were suddenly

AD-3
increased by say 10 degrees, then curves like those in Fig. A-1, but for all

points of interest in the book, could be used to calculate the change in A at

those points. It is, of course, necessary to know the activation energy and the

coefficient kg , but these are available for many of the properties of interest, or could be measured. Again, this could be done for other properties of

interest, provided only that the rate law is known, as well as the change with

temperature of the rate constant. Average values of the change in property are also easily calculated, but it is felt here that this is not a very useful

quantity.

With this in mind, and with the data in the figures, what can be said in

a general way about the difference in the rate of reaction between the surface

regions and the interior central regions of the book? Consider the following

idealized situation. A book is placed in an environment in which the

temperature fluctuates in a regular, systematic manner. Half the time the

temperature is Tg+AT and half the time it is Tg-AT. The average temperature is

then Tg . Further to simplify the problem and the reasoning, assume that steady

state has been reached, and that the book is big enough, or the cycle time

short enough, that the center of the book is essentially always at the average

temperature. Now consider a given degradation reaction. At the center of the

book, the reaction will proceed at a constant rate. In the surface regions of

the book, and particularly at the edges and corners of the pages, the situation

is quite different. Here the temperature follows the ambient temperature, the

more closely the nearer the location is to the very surface of the book. On the

high temperature part of the cycle, the reaction will occur more rapidly than

in the interior, while on the low temperature part the reaction will occur less

rapidly than in the interior. However, because of the exponential Arrhenius

dependence of the rate constant on temperature, the net effect is that the

extent of reaction in the surface regions will always be greater than in the

center portion of the book. While this can be shown analytically, it can also

be reasoned in the following manner. Suppose the reaction rate constant at

Tg+AT is just twice what it is at Tg . (For an activation energy of 30kCal, as for specific absorption (5), AT is 4.16K.). And consider one cycle of the

temperature scheme outlined above. Then, the center portion of the book spends

the full cycle at the temperature Tg , and the surface spends 1/2 cycle at Tg+AT

and 1/2 cycle at Tg-AT, However, in the 1/2 cycle at Tg+AT, as much reaction

occurs as in one full cycle at Tg . In addition, at Tg-AT, reaction still

proceeds, albeit at a reduced rate of about 1/2 that at Tg . The amount of

reaction that occurs at this lower temperature is the added extent of reaction

that occurs at the surface of the book as compared to the center. Thus, the

extent of reaction at the surface of the book is greater than in the center.

Actual calculations for Tg=298K, AT=4.16, with an activation energy of 30kCal

show, in relative units, the extent of reaction in the interior is 1.38, while

at the edges of the pages, which follow the ambient temperature, the extent of

reaction is 1.72.

How much this effect has to do with the yellow discoloration borders on

the edges of book pages is not known, but it could very well be a contributing

factor. As discussed in the main body of the report, diffusion of pollutant

into the book is also very likely a contributing factor, and it is to be

noted that the temperature and pollutant act synergistically

AD-4
A. 2.1 Conclusions

1 . In books or document boxes , the variation in temperature as the

exterior temperature varies is greater in the surface regions than in the

central regions of the item. Knowing the dimensions and the thermal

diffusivity of the item, the variation of temperature with time at any

position in the item can be calculated, at least approximately.

2. The measurement of temperatures in an item like a book or document box

following a sudden change in the exterior temperature are easy

measurements to make and would be instructive.

3 . Because of the Arrhenius dependence of rate constants on temperature

in a fluctuating temperature environment the extent of reaction in the

surface regions of books and document boxes will be greater than in the

central regions of the item.

A. 3 The Water Vapor Microenvironment

The water vapor microenvironment, usually characterized by the relative

humidity, is important because it determines the moisture content of the

records. This latter is an important quantity, particularly with paper,

because, as discussed in the main text, one of the principal degradation

reactions of paper is hydrolysis, the rate of which is proportional to the

moisture concentration, and at the higher moisture contents, microorganisms can

grow (6). It is thus important to analyze the water vapor microenvironment as was done in the main text for pollutants. Indeed, the same techniques can be

used for water vapor as for pollutants, but with some added qualifications, as . will be discussed in what follows.

First-,- it is important to recognize that, for pollutants, the principal

function of a container was to keep pollutants out. This could be done with a sealed, impermeable container (which led to complications, as discussed in the

text)or with one that reacted with the pollutants and thus acted as a "scavenger”. With water vapor, shielding of the contents by impermeable

containers might not be practical, because of the initial conditions. If, for

example, docioments with a high moisture content were sealed in an impermeable

container, then the moisture content would remain sensibly constant, their rate

of degradatiqn would be relatively high, and they might be subject to

microorganisms. Hence, with water vapor, it would be better to provide water

vapor access between the interior of the container and the exterior, assuming a reasonable control of the exterior Rh.

The analysis of the transport of water vapor between the interior and

exterior of a container follows the same analysis as was used for pollutants.

In this case, however, no reaction is considered in either the contents or the

walls of the container. The reason is that paper at normal Rh contains such a large amount of water that its concentration will not be changed a great deal

as hydrolysis takes place. (Note that at 4% regain, the mole fraction of water

in cellulose, based on cellulose monomers, is 0.27, and that a change in the

degree of polymerization involves only a very few hydrolytic attacks per

AD-5
cellulose molecule . ) Now, in the analysis of microenvironments with

pollutants, a relaxation time was developed. Its magnitude was given by Vi/ADS,

where V is the total volume of the container (including the volume at STP of

the pollutant in solution in the contents) , i is the thickness of the container

walls, A their area, D their diffusion constant, and S the solubility of

pollutant in them as defined in Appendix A-1. This quantity is a measure of

the time necessary for the interior and exterior of a container to come to

equilibrium following a sudden change in the conditions in one of them. The

same analysis as for pollutants applies to water vapor, and in what follows we will principally discuss the value of this relaxation time for water vapor,

comparing its value to those developed for pollutants.

There are two material constants in the relaxation time: D and S. They

will vary with the material of the container wall and with the gas or vapor. We

will discuss S, the solubility parameter first.

The quantity S, as defined in Appendix A-1, is the concentration in

cm^ (STP)/cm^ in the solid phase divided by the mole fraction in the gas phase,

all at one atmosphere pressure. For the cellulose-water vapor system, this

quantity is not a constant, because the regain curve is not linear over its

whole range. Direct calculations from the data of Jeffries for unbleached

spruce sulfite pulp (7) show that S varies from 11,200 at 5% Rh to 3780 at 80%

Rh. However, in the region from 30% to 70% Rh, the regain curve is quite

linear, and S varies from 4340 to 3650. Hence, as an approximation, we may take

S to be 4000 in this Rh range. The magnitude of this quantity will be discussed

below.

In contrast to cellulose, polyethylene (PE) and polypropylene (PP) have

values of S of 2.5 and 2.9, respectively ( 8 ). This is totally in accord with

expectation; water is essentially insoluble in the two polyolefin polymers, but

quite soluble in the anhydroglucose polymer.

The other material property we need is the diffusion constant, D. For PE

and PP, these are known, and are the high values of 230x10"® and 240x10*®

cm^/sec, respectively. For cellulose in the form of paper, we have been unable

to find any data on diffusion constant for water. There are, however, data on

regenerated cellulose. The most complete study was done by Newns(9), who

determined values for D of less than 10"® at low moisture contents, to values

greater than 10"® at high moisture contents, higher than those normally found

in paper. How paper would compare to this is unknown. Considering that paper is a looser structure than regenerated cellulose, and purely for purposes of

illustration, we have chosen a value of 10"® cm^/sec. This could be in

considerable error. Then, it is to be noted that only the product DS appears in

the expression for r . All these data have been collected in Table A-1, where

there are also listed the values for SO2 used previously.

While the data for PE an PP are fairly sound, the data for paper, except

for S, are undoubtedly not quantitatively correct. Nevertheless, the

qualitative trend is in accord with expectation. First note the values for S.

As previously mentioned, these indicate that S for water vapor in paper is more

than 1060 times as great as it is for water in PE or PP. Also note that S for

water vapor in paper is more than 100 times as great as for SOj in paper. These

AD -
are probably fairly well established and are in accord with expectations. The

diffusion constants in paper have already been discussed and are not well

established, but those for PE and PP are actual literature values (8) . The

uncertainty in the values of DS then stems largely from the uncertainty in the

values of D for paper. This is as expected, since this is the hardest quantity

to determine.

We now discuss the significance of these results. Recall that the product

DS enters into the denominator of the expression for the relaxation time.

Hence, from this factor alone, an increase in this means a shortening of the

relaxation time. Thus, comparing emotv paperboard containers without gaps for

water and SO2 , it is seen that with water vapor the interior of the container

comes into equilibrium with the exterior 100 to 1000 times as rapidly as it

does for SO2. Similarly, for emotv containers and water vapor, the paperboard

container comes into equilibrium nearly 1000 times as fast as similar

containers made of PE or PP. Because of the uncertainties in the diffusion

constant, as previously discussed, the quantitative values may be incorrect,

but the trend is certainly correct.

If, however the container contains paper documents, even loosely packed

so that equilibrium between them and the interior environment of the container

always obtains, the situation is quite different. This is because of the volume

V in the numerator of the expression for the relaxation time. Recall that this

V was the empty volume plus the volume of gas or vapor in solution in the

contents (See Appendix A-1). Now, assuming a reasonable quantity of paper

documents in the container (of the order of half full) , the volume of water

vapor in the contents far exceeds the unoccupied volume in the container. In

this case, V =* SV^ , where is the volume of the contents. Now consider the

paperboard container. Here we may safely assimie that S is the same for the

contents as for the wails. In this case, the relaxation time is independent of

S, and, compared to the empty container, is approximately S times as great

(4000 for our specific example) . Now consider the case of the container with

polyolefin wails. Here again the relaxation times compared to the empty

container increase by a factor of the value of S for the contents. In effect,

the high solubility of water vapor in the container contents increases the

volume of the container several thousand fold, and that much more water vapor

must diffuse through the walls to obtain equilibrium. This water vapor

stabilizing effect of paper is well known, and was used in the design of the

Constitution and Declaration of Independence cases, which contain a thick layer

of pure a cellulose.

A. 3.1

1) Because the initial moisture content of documents to be boxed is not

necessarily controlled, impermeable containers are not practical for

controlling moisture content.

2) The high solubility of water vapor in cellulose dramatically lowers

the rate at which the interior of a box filled with cellulosic documents

comes into equilibrium with the external environment as compared to an empty box.

AD-7
ADDENDUM REFERENCES

1. American Institute of Physics Handbook, D. E. Gray, Ed. McGraw-Hill,

1957, p. 4-69

2. Encyclopedia of Polymer Science and Technology, Interscience, 1970,

Vol. 13, p. 780

3. R. V, Churchill, "Fourier Series and Boundary Value Problems", McGrawHill, 1941

4. H. S. Carls law and J. C. Jaeger, "Conduction of Heat in Solids",

Clarendon Press, Oxford, 1976, p. 185

5. B. L. Browning and W. A. Wink, "Studies on the Permanence and

Durability of Paper I. Prediction of Paper Permanence", TAPPI 51(4') . 156-

163(1968)

6. C. Shahani and W. K. Wilson, "Preservation of Libraries and

Archives", American Scientist 21. 240-251(1987)

7. R. Jeffries, J. Textile Inst. T339(1960)

8. J. Crank and G. S. Park, "Diffusion in Polymers", Academic Press, NY,

1968

9. Ao C. Newns , "The Sorption and Desorption Kinetics of Water in a Regenerated Cellulose", J. Polymer Sci. XLI . 425-434(1959)

AD-8
TABLE A-1

Solubility and Diffusion Constant for Water Vapor

Material S D, cm^/sec, xlO^ DS , cm^/sec, xlO^

Paper 4000 10® 400

PE m

CM 230 5.8

PP 2.9 240 7

Paper (SO2 ) 30 1-10 0.3-

a. Little more than a guess

AD-9
ADDENDUM FIGURE CAPTIONS

Fig. A-1 Reduced temperature at various locations along the

shortest dimension of a book at various times after a sudden

change in the external temperature. To obtain the actual

temperature change, the ordinate should be multiplied by the

magnitude of the sudden temperature change.

Fig. A-2 Same as Fig. A-1 but for a completely filled document box

of the same dimensions as the prototypical container.

Fig. A- 3. Samer as Fig. A-1 but for a shelf of books. The'

locations are at the center of the stack of books along the

shortest dimension.

AD-10
Fig. A1

POSITION, cm.
(T

-

Te)/(To

- Te)

Fig. A2

POSITION, cm
Fig. A3

POSITION, cm.
NBS»114A (REV. 2 -ac) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

4. TITLE AND SUBTITLE

1. PUBLICATION OR 2 REPORT NO.

NBSIR 87-3635

. Performing Organ. Report NoJ 3. Publication Date

The Characterization of Microenvironments and the Degradation of Archival

Records: A Research Program

5. AUTHOR(S)

Elio Passaglia

6. PERFORMING ORGANIZATION (If joint or other than N BS, see instructions) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, State, ZIP)

10.

SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gnificant

bibliography or literature survey, mention it here)

Air pollutants increase the rate of degradation of documents and records

in archival storage. However, with the exception of books, most of these documents

and records are not exposed to the ambient environment of the archive stacks.

They are instead stored in containers of various kinds. The records therefore

experience the microenvironment of the interior of the container, which may be

more benign than the macroenvironment exterior to it. In this report, the

environment inside a container, and any changes that can occur in it as the

exterior environment changes, is modelled. On the basis of this modelling, and

what is know about the effects of pollutants on the degradation of archival

records, a research program designed to lead to an understanding of the maximum

benefit that could be obtained with various containers is laid out. The design

and materials of construction are specifically discussed.

12.

KEY WORDS (S/x to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) Air pollutants; archival records; degradation; diffusion; lifetime testing;

microenvironments

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